4(x-2)(x-2)-2*2(x-1)=4

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Solution for 4(x-2)(x-2)-2*2(x-1)=4 equation: 


Simplifying
4(x + -2)(x + -2) + -2 * 2(x + -1) = 4

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

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

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

Combine like terms: -2x + -2x = -4x
4(4 + -4x + x2) + -2 * 2(x + -1) = 4
(4 * 4 + -4x * 4 + x2 * 4) + -2 * 2(x + -1) = 4
(16 + -16x + 4x2) + -2 * 2(x + -1) = 4

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

Multiply -2 * 2
16 + -16x + 4x2 + -4(-1 + x) = 4
16 + -16x + 4x2 + (-1 * -4 + x * -4) = 4
16 + -16x + 4x2 + (4 + -4x) = 4

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

Combine like terms: 16 + 4 = 20
20 + -16x + -4x + 4x2 = 4

Combine like terms: -16x + -4x = -20x
20 + -20x + 4x2 = 4

Solving
20 + -20x + 4x2 = 4

Solving for variable 'x'.

Reorder the terms:
20 + -4 + -20x + 4x2 = 4 + -4

Combine like terms: 20 + -4 = 16
16 + -20x + 4x2 = 4 + -4

Combine like terms: 4 + -4 = 0
16 + -20x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(4 + -5x + x2) = 0

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

Ignore the factor 4.

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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

Simplifying
x = 1

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 = {1, 4}

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