(2x-1)(2x-1)=-8(2x+1)

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Solution for (2x-1)(2x-1)=-8(2x+1) equation: 


Simplifying
(2x + -1)(2x + -1) = -8(2x + 1)

Reorder the terms:
(-1 + 2x)(2x + -1) = -8(2x + 1)

Reorder the terms:
(-1 + 2x)(-1 + 2x) = -8(2x + 1)

Multiply (-1 + 2x) * (-1 + 2x)
(-1(-1 + 2x) + 2x * (-1 + 2x)) = -8(2x + 1)
((-1 * -1 + 2x * -1) + 2x * (-1 + 2x)) = -8(2x + 1)
((1 + -2x) + 2x * (-1 + 2x)) = -8(2x + 1)
(1 + -2x + (-1 * 2x + 2x * 2x)) = -8(2x + 1)
(1 + -2x + (-2x + 4x2)) = -8(2x + 1)

Combine like terms: -2x + -2x = -4x
(1 + -4x + 4x2) = -8(2x + 1)

Reorder the terms:
1 + -4x + 4x2 = -8(1 + 2x)
1 + -4x + 4x2 = (1 * -8 + 2x * -8)
1 + -4x + 4x2 = (-8 + -16x)

Solving
1 + -4x + 4x2 = -8 + -16x

Solving for variable 'x'.

Reorder the terms:
1 + 8 + -4x + 16x + 4x2 = -8 + -16x + 8 + 16x

Combine like terms: 1 + 8 = 9
9 + -4x + 16x + 4x2 = -8 + -16x + 8 + 16x

Combine like terms: -4x + 16x = 12x
9 + 12x + 4x2 = -8 + -16x + 8 + 16x

Reorder the terms:
9 + 12x + 4x2 = -8 + 8 + -16x + 16x

Combine like terms: -8 + 8 = 0
9 + 12x + 4x2 = 0 + -16x + 16x
9 + 12x + 4x2 = -16x + 16x

Combine like terms: -16x + 16x = 0
9 + 12x + 4x2 = 0

Factor a trinomial.
(3 + 2x)(3 + 2x) = 0


Subproblem 1
Set the factor '(3 + 2x)' equal to zero and attempt to solve:

Simplifying
3 + 2x = 0

Solving
3 + 2x = 0

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

Add '-3' to each side of the equation.
3 + -3 + 2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2x = 0 + -3
2x = 0 + -3

Combine like terms: 0 + -3 = -3
2x = -3

Divide each side by '2'.
x = -1.5

Simplifying
x = -1.5

Subproblem 2
Set the factor '(3 + 2x)' equal to zero and attempt to solve:

Simplifying
3 + 2x = 0

Solving
3 + 2x = 0

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

Add '-3' to each side of the equation.
3 + -3 + 2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2x = 0 + -3
2x = 0 + -3

Combine like terms: 0 + -3 = -3
2x = -3

Divide each side by '2'.
x = -1.5

Simplifying
x = -1.5
Solution
x = {-1.5, -1.5}

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