2(x-1)(x-1)+3=11

Solution for 2(x-1)(x-1)+3=11 equation:

Simplifying
2(x + -1)(x + -1) + 3 = 11

Reorder the terms:
2(-1 + x)(x + -1) + 3 = 11

Reorder the terms:
2(-1 + x)(-1 + x) + 3 = 11

Multiply (-1 + x) * (-1 + x)
2(-1(-1 + x) + x(-1 + x)) + 3 = 11
2((-1 * -1 + x * -1) + x(-1 + x)) + 3 = 11
2((1 + -1x) + x(-1 + x)) + 3 = 11
2(1 + -1x + (-1 * x + x * x)) + 3 = 11
2(1 + -1x + (-1x + x2)) + 3 = 11

Combine like terms: -1x + -1x = -2x
2(1 + -2x + x2) + 3 = 11
(1 * 2 + -2x * 2 + x2 * 2) + 3 = 11
(2 + -4x + 2x2) + 3 = 11

Reorder the terms:
2 + 3 + -4x + 2x2 = 11

Combine like terms: 2 + 3 = 5
5 + -4x + 2x2 = 11

Solving
5 + -4x + 2x2 = 11

Solving for variable 'x'.

Reorder the terms:
5 + -11 + -4x + 2x2 = 11 + -11

Combine like terms: 5 + -11 = -6
-6 + -4x + 2x2 = 11 + -11

Combine like terms: 11 + -11 = 0
-6 + -4x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + -2x + x2) = 0

Factor a trinomial.
2((-1 + -1x)(3 + -1x)) = 0

Ignore the factor 2.
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 '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-1, 3}