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

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


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

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

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

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

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

Solving
36 + -24x + 4x2 = 4

Solving for variable 'x'.

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

Combine like terms: 36 + -4 = 32
32 + -24x + 4x2 = 4 + -4

Combine like terms: 4 + -4 = 0
32 + -24x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(8 + -6x + x2) = 0

Factor a trinomial.
4((2 + -1x)(4 + -1x)) = 0

Ignore the factor 4.

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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

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

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

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

Divide each side by '-1'.
x = 2

Simplifying
x = 2

Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {2, 4}

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