4(y-1)(y-1)-9=0

Solution for 4(y-1)(y-1)-9=0 equation:

Simplifying
4(y + -1)(y + -1) + -9 = 0

Reorder the terms:
4(-1 + y)(y + -1) + -9 = 0

Reorder the terms:
4(-1 + y)(-1 + y) + -9 = 0

Multiply (-1 + y) * (-1 + y)
4(-1(-1 + y) + y(-1 + y)) + -9 = 0
4((-1 * -1 + y * -1) + y(-1 + y)) + -9 = 0
4((1 + -1y) + y(-1 + y)) + -9 = 0
4(1 + -1y + (-1 * y + y * y)) + -9 = 0
4(1 + -1y + (-1y + y2)) + -9 = 0

Combine like terms: -1y + -1y = -2y
4(1 + -2y + y2) + -9 = 0
(1 * 4 + -2y * 4 + y2 * 4) + -9 = 0
(4 + -8y + 4y2) + -9 = 0

Reorder the terms:
4 + -9 + -8y + 4y2 = 0

Combine like terms: 4 + -9 = -5
-5 + -8y + 4y2 = 0

Solving
-5 + -8y + 4y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(-1 + -2y)(5 + -2y) = 0

Subproblem 1
Set the factor '(-1 + -2y)' equal to zero and attempt to solve:

Simplifying
-1 + -2y = 0

Solving
-1 + -2y = 0

Move all terms containing y to the left, all other terms to the right.

Add '1' to each side of the equation.
-1 + 1 + -2y = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -2y = 0 + 1
-2y = 0 + 1

Combine like terms: 0 + 1 = 1
-2y = 1

Divide each side by '-2'.
y = -0.5

Simplifying
y = -0.5
Subproblem 2
Set the factor '(5 + -2y)' equal to zero and attempt to solve:

Simplifying
5 + -2y = 0

Solving
5 + -2y = 0

Move all terms containing y to the left, all other terms to the right.

Add '-5' to each side of the equation.
5 + -5 + -2y = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2y = 0 + -5
-2y = 0 + -5

Combine like terms: 0 + -5 = -5
-2y = -5

Divide each side by '-2'.
y = 2.5

Simplifying
y = 2.5
Solution
y = {-0.5, 2.5}