2(x-1)(x-1)-9(x-1)-5=0

Solution for 2(x-1)(x-1)-9(x-1)-5=0 equation:

Simplifying
2(x + -1)(x + -1) + -9(x + -1) + -5 = 0

Reorder the terms:
2(-1 + x)(x + -1) + -9(x + -1) + -5 = 0

Reorder the terms:
2(-1 + x)(-1 + x) + -9(x + -1) + -5 = 0

Multiply (-1 + x) * (-1 + x)
2(-1(-1 + x) + x(-1 + x)) + -9(x + -1) + -5 = 0
2((-1 * -1 + x * -1) + x(-1 + x)) + -9(x + -1) + -5 = 0
2((1 + -1x) + x(-1 + x)) + -9(x + -1) + -5 = 0
2(1 + -1x + (-1 * x + x * x)) + -9(x + -1) + -5 = 0
2(1 + -1x + (-1x + x2)) + -9(x + -1) + -5 = 0

Combine like terms: -1x + -1x = -2x
2(1 + -2x + x2) + -9(x + -1) + -5 = 0
(1 * 2 + -2x * 2 + x2 * 2) + -9(x + -1) + -5 = 0
(2 + -4x + 2x2) + -9(x + -1) + -5 = 0

Reorder the terms:
2 + -4x + 2x2 + -9(-1 + x) + -5 = 0
2 + -4x + 2x2 + (-1 * -9 + x * -9) + -5 = 0
2 + -4x + 2x2 + (9 + -9x) + -5 = 0

Reorder the terms:
2 + 9 + -5 + -4x + -9x + 2x2 = 0

Combine like terms: 2 + 9 = 11
11 + -5 + -4x + -9x + 2x2 = 0

Combine like terms: 11 + -5 = 6
6 + -4x + -9x + 2x2 = 0

Combine like terms: -4x + -9x = -13x
6 + -13x + 2x2 = 0

Solving
6 + -13x + 2x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(1 + -2x)(6 + -1x) = 0

Subproblem 1
Set the factor '(1 + -2x)' equal to zero and attempt to solve:

Simplifying
1 + -2x = 0

Solving
1 + -2x = 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 + -2x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2x = 0 + -1
-2x = 0 + -1

Combine like terms: 0 + -1 = -1
-2x = -1

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5
Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {0.5, 6}