(2x-6)(2x-6)=4x+36

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Solution for (2x-6)(2x-6)=4x+36 equation: 


Simplifying
(2x + -6)(2x + -6) = 4x + 36

Reorder the terms:
(-6 + 2x)(2x + -6) = 4x + 36

Reorder the terms:
(-6 + 2x)(-6 + 2x) = 4x + 36

Multiply (-6 + 2x) * (-6 + 2x)
(-6(-6 + 2x) + 2x * (-6 + 2x)) = 4x + 36
((-6 * -6 + 2x * -6) + 2x * (-6 + 2x)) = 4x + 36
((36 + -12x) + 2x * (-6 + 2x)) = 4x + 36
(36 + -12x + (-6 * 2x + 2x * 2x)) = 4x + 36
(36 + -12x + (-12x + 4x2)) = 4x + 36

Combine like terms: -12x + -12x = -24x
(36 + -24x + 4x2) = 4x + 36

Reorder the terms:
36 + -24x + 4x2 = 36 + 4x

Add '-36' to each side of the equation.
36 + -24x + -36 + 4x2 = 36 + -36 + 4x

Reorder the terms:
36 + -36 + -24x + 4x2 = 36 + -36 + 4x

Combine like terms: 36 + -36 = 0
0 + -24x + 4x2 = 36 + -36 + 4x
-24x + 4x2 = 36 + -36 + 4x

Combine like terms: 36 + -36 = 0
-24x + 4x2 = 0 + 4x
-24x + 4x2 = 4x

Solving
-24x + 4x2 = 4x

Solving for variable 'x'.

Reorder the terms:
-24x + -4x + 4x2 = 4x + -4x

Combine like terms: -24x + -4x = -28x
-28x + 4x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
-28x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4x'.
4x(-7 + 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 '(-7 + x)' equal to zero and attempt to solve:

Simplifying
-7 + x = 0

Solving
-7 + x = 0

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

Add '7' to each side of the equation.
-7 + 7 + x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + x = 0 + 7
x = 0 + 7

Combine like terms: 0 + 7 = 7
x = 7

Simplifying
x = 7
Solution
x = {0, 7}

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