(x-2)(x-2)+3=12

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Solution for (x-2)(x-2)+3=12 equation: 


Simplifying
(x + -2)(x + -2) + 3 = 12

Reorder the terms:
(-2 + x)(x + -2) + 3 = 12

Reorder the terms:
(-2 + x)(-2 + x) + 3 = 12

Multiply (-2 + x) * (-2 + x)
(-2(-2 + x) + x(-2 + x)) + 3 = 12
((-2 * -2 + x * -2) + x(-2 + x)) + 3 = 12
((4 + -2x) + x(-2 + x)) + 3 = 12
(4 + -2x + (-2 * x + x * x)) + 3 = 12
(4 + -2x + (-2x + x2)) + 3 = 12

Combine like terms: -2x + -2x = -4x
(4 + -4x + x2) + 3 = 12

Reorder the terms:
4 + 3 + -4x + x2 = 12

Combine like terms: 4 + 3 = 7
7 + -4x + x2 = 12

Solving
7 + -4x + x2 = 12

Solving for variable 'x'.

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

Combine like terms: 7 + -12 = -5
-5 + -4x + x2 = 12 + -12

Combine like terms: 12 + -12 = 0
-5 + -4x + x2 = 0

Factor a trinomial.
(-1 + -1x)(5 + -1x) = 0


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 '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {-1, 5}

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