(x-2)(x-2)4=0

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Solution for (x-2)(x-2)4=0 equation: 


Simplifying
(x + -2)(x + -2) * 4 = 0

Reorder the terms:
(-2 + x)(x + -2) * 4 = 0

Reorder the terms:
(-2 + x)(-2 + x) * 4 = 0

Reorder the terms for easier multiplication:
4(-2 + x)(-2 + x) = 0

Multiply (-2 + x) * (-2 + x)
4(-2(-2 + x) + x(-2 + x)) = 0
4((-2 * -2 + x * -2) + x(-2 + x)) = 0
4((4 + -2x) + x(-2 + x)) = 0
4(4 + -2x + (-2 * x + x * x)) = 0
4(4 + -2x + (-2x + x2)) = 0

Combine like terms: -2x + -2x = -4x
4(4 + -4x + x2) = 0
(4 * 4 + -4x * 4 + x2 * 4) = 0
(16 + -16x + 4x2) = 0

Solving
16 + -16x + 4x2 = 0

Solving for variable 'x'.

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

Factor a trinomial.
4((2 + -1x)(2 + -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 '(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
Solution
x = {2, 2}

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