(2x-3)(2x-3)-16=-7

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Solution for (2x-3)(2x-3)-16=-7 equation: 


Simplifying
(2x + -3)(2x + -3) + -16 = -7

Reorder the terms:
(-3 + 2x)(2x + -3) + -16 = -7

Reorder the terms:
(-3 + 2x)(-3 + 2x) + -16 = -7

Multiply (-3 + 2x) * (-3 + 2x)
(-3(-3 + 2x) + 2x * (-3 + 2x)) + -16 = -7
((-3 * -3 + 2x * -3) + 2x * (-3 + 2x)) + -16 = -7
((9 + -6x) + 2x * (-3 + 2x)) + -16 = -7
(9 + -6x + (-3 * 2x + 2x * 2x)) + -16 = -7
(9 + -6x + (-6x + 4x2)) + -16 = -7

Combine like terms: -6x + -6x = -12x
(9 + -12x + 4x2) + -16 = -7

Reorder the terms:
9 + -16 + -12x + 4x2 = -7

Combine like terms: 9 + -16 = -7
-7 + -12x + 4x2 = -7

Add '7' to each side of the equation.
-7 + -12x + 7 + 4x2 = -7 + 7

Reorder the terms:
-7 + 7 + -12x + 4x2 = -7 + 7

Combine like terms: -7 + 7 = 0
0 + -12x + 4x2 = -7 + 7
-12x + 4x2 = -7 + 7

Combine like terms: -7 + 7 = 0
-12x + 4x2 = 0

Solving
-12x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4x'.
4x(-3 + x) = 0

Ignore the factor 4.

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

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

Simplifying
-3 + x = 0

Solving
-3 + x = 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 + x = 0 + 3

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

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

Simplifying
x = 3
Solution
x = {0, 3}

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