(x-1)(x-1)-5(x-1)-6=0

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Solution for (x-1)(x-1)-5(x-1)-6=0 equation: 


Simplifying
(x + -1)(x + -1) + -5(x + -1) + -6 = 0

Reorder the terms:
(-1 + x)(x + -1) + -5(x + -1) + -6 = 0

Reorder the terms:
(-1 + x)(-1 + x) + -5(x + -1) + -6 = 0

Multiply (-1 + x) * (-1 + x)
(-1(-1 + x) + x(-1 + x)) + -5(x + -1) + -6 = 0
((-1 * -1 + x * -1) + x(-1 + x)) + -5(x + -1) + -6 = 0
((1 + -1x) + x(-1 + x)) + -5(x + -1) + -6 = 0
(1 + -1x + (-1 * x + x * x)) + -5(x + -1) + -6 = 0
(1 + -1x + (-1x + x2)) + -5(x + -1) + -6 = 0

Combine like terms: -1x + -1x = -2x
(1 + -2x + x2) + -5(x + -1) + -6 = 0

Reorder the terms:
1 + -2x + x2 + -5(-1 + x) + -6 = 0
1 + -2x + x2 + (-1 * -5 + x * -5) + -6 = 0
1 + -2x + x2 + (5 + -5x) + -6 = 0

Reorder the terms:
1 + 5 + -6 + -2x + -5x + x2 = 0

Combine like terms: 1 + 5 = 6
6 + -6 + -2x + -5x + x2 = 0

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

Combine like terms: -2x + -5x = -7x
-7x + x2 = 0

Solving
-7x + x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-7 + x) = 0


Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(-7 + x)' equal to zero and attempt to solve:

Simplifying
-7 + x = 0

Solving
-7 + x = 0

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

Add '7' to each side of the equation.
-7 + 7 + x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + x = 0 + 7
x = 0 + 7

Combine like terms: 0 + 7 = 7
x = 7

Simplifying
x = 7
Solution
x = {0, 7}

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