(x-1)(x-1)+3=12

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Solution for (x-1)(x-1)+3=12 equation: 


Simplifying
(x + -1)(x + -1) + 3 = 12

Reorder the terms:
(-1 + x)(x + -1) + 3 = 12

Reorder the terms:
(-1 + x)(-1 + x) + 3 = 12

Multiply (-1 + x) * (-1 + x)
(-1(-1 + x) + x(-1 + x)) + 3 = 12
((-1 * -1 + x * -1) + x(-1 + x)) + 3 = 12
((1 + -1x) + x(-1 + x)) + 3 = 12
(1 + -1x + (-1 * x + x * x)) + 3 = 12
(1 + -1x + (-1x + x2)) + 3 = 12

Combine like terms: -1x + -1x = -2x
(1 + -2x + x2) + 3 = 12

Reorder the terms:
1 + 3 + -2x + x2 = 12

Combine like terms: 1 + 3 = 4
4 + -2x + x2 = 12

Solving
4 + -2x + x2 = 12

Solving for variable 'x'.

Reorder the terms:
4 + -12 + -2x + x2 = 12 + -12

Combine like terms: 4 + -12 = -8
-8 + -2x + x2 = 12 + -12

Combine like terms: 12 + -12 = 0
-8 + -2x + x2 = 0

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


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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