# 8y(2y-3)=9

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## Solution for 8y(2y-3)=9 equation:

Simplifying
8y(2y + -3) = 9
Reorder the terms:
8y(-3 + 2y) = 9
(-3 * 8y + 2y * 8y) = 9
(-24y + 16y2) = 9
Solving
-24y + 16y2 = 9
Solving for variable 'y'.
Reorder the terms:
-9 + -24y + 16y2 = 9 + -9
Combine like terms: 9 + -9 = 0
-9 + -24y + 16y2 = 0
Begin completing the square. Divide all terms by
16 the coefficient of the squared term:
Divide each side by '16'.
-0.5625 + -1.5y + y2 = 0
Move the constant term to the right:
Add '0.5625' to each side of the equation.
-0.5625 + -1.5y + 0.5625 + y2 = 0 + 0.5625
Reorder the terms:
-0.5625 + 0.5625 + -1.5y + y2 = 0 + 0.5625
Combine like terms: -0.5625 + 0.5625 = 0.0000
0.0000 + -1.5y + y2 = 0 + 0.5625
-1.5y + y2 = 0 + 0.5625
Combine like terms: 0 + 0.5625 = 0.5625
-1.5y + y2 = 0.5625
The y term is -1.5y. Take half its coefficient (-0.75).
Square it (0.5625) and add it to both sides.
Add '0.5625' to each side of the equation.
-1.5y + 0.5625 + y2 = 0.5625 + 0.5625
Reorder the terms:
0.5625 + -1.5y + y2 = 0.5625 + 0.5625
Combine like terms: 0.5625 + 0.5625 = 1.125
0.5625 + -1.5y + y2 = 1.125
Factor a perfect square on the left side:
(y + -0.75)(y + -0.75) = 1.125
Calculate the square root of the right side: 1.060660172
Break this problem into two subproblems by setting
(y + -0.75) equal to 1.060660172 and -1.060660172.
Subproblem 1y + -0.75 = 1.060660172
Simplifying
y + -0.75 = 1.060660172
Reorder the terms:
-0.75 + y = 1.060660172
Solving
-0.75 + y = 1.060660172
Solving for variable 'y'.
Move all terms containing y to the left, all other terms to the right.
Add '0.75' to each side of the equation.
-0.75 + 0.75 + y = 1.060660172 + 0.75
Combine like terms: -0.75 + 0.75 = 0.00
0.00 + y = 1.060660172 + 0.75
y = 1.060660172 + 0.75
Combine like terms: 1.060660172 + 0.75 = 1.810660172
y = 1.810660172
Simplifying
y = 1.810660172
Subproblem 2y + -0.75 = -1.060660172
Simplifying
y + -0.75 = -1.060660172
Reorder the terms:
-0.75 + y = -1.060660172
Solving
-0.75 + y = -1.060660172
Solving for variable 'y'.
Move all terms containing y to the left, all other terms to the right.
Add '0.75' to each side of the equation.
-0.75 + 0.75 + y = -1.060660172 + 0.75
Combine like terms: -0.75 + 0.75 = 0.00
0.00 + y = -1.060660172 + 0.75
y = -1.060660172 + 0.75
Combine like terms: -1.060660172 + 0.75 = -0.310660172
y = -0.310660172
Simplifying
y = -0.310660172
SolutionThe solution to the problem is based on the solutions
from the subproblems.
y = {1.810660172, -0.310660172}`