11(x-2)+(x-5)=(x+2)(x-6)

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Solution for 11(x-2)+(x-5)=(x+2)(x-6) equation: 


Simplifying
11(x + -2) + (x + -5) = (x + 2)(x + -6)

Reorder the terms:
11(-2 + x) + (x + -5) = (x + 2)(x + -6)
(-2 * 11 + x * 11) + (x + -5) = (x + 2)(x + -6)
(-22 + 11x) + (x + -5) = (x + 2)(x + -6)

Reorder the terms:
-22 + 11x + (-5 + x) = (x + 2)(x + -6)

Remove parenthesis around (-5 + x)
-22 + 11x + -5 + x = (x + 2)(x + -6)

Reorder the terms:
-22 + -5 + 11x + x = (x + 2)(x + -6)

Combine like terms: -22 + -5 = -27
-27 + 11x + x = (x + 2)(x + -6)

Combine like terms: 11x + x = 12x
-27 + 12x = (x + 2)(x + -6)

Reorder the terms:
-27 + 12x = (2 + x)(x + -6)

Reorder the terms:
-27 + 12x = (2 + x)(-6 + x)

Multiply (2 + x) * (-6 + x)
-27 + 12x = (2(-6 + x) + x(-6 + x))
-27 + 12x = ((-6 * 2 + x * 2) + x(-6 + x))
-27 + 12x = ((-12 + 2x) + x(-6 + x))
-27 + 12x = (-12 + 2x + (-6 * x + x * x))
-27 + 12x = (-12 + 2x + (-6x + x2))

Combine like terms: 2x + -6x = -4x
-27 + 12x = (-12 + -4x + x2)

Solving
-27 + 12x = -12 + -4x + x2

Solving for variable 'x'.

Reorder the terms:
-27 + 12 + 12x + 4x + -1x2 = -12 + -4x + x2 + 12 + 4x + -1x2

Combine like terms: -27 + 12 = -15
-15 + 12x + 4x + -1x2 = -12 + -4x + x2 + 12 + 4x + -1x2

Combine like terms: 12x + 4x = 16x
-15 + 16x + -1x2 = -12 + -4x + x2 + 12 + 4x + -1x2

Reorder the terms:
-15 + 16x + -1x2 = -12 + 12 + -4x + 4x + x2 + -1x2

Combine like terms: -12 + 12 = 0
-15 + 16x + -1x2 = 0 + -4x + 4x + x2 + -1x2
-15 + 16x + -1x2 = -4x + 4x + x2 + -1x2

Combine like terms: -4x + 4x = 0
-15 + 16x + -1x2 = 0 + x2 + -1x2
-15 + 16x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-15 + 16x + -1x2 = 0

Factor a trinomial.
(-15 + x)(1 + -1x) = 0


Subproblem 1
Set the factor '(-15 + x)' equal to zero and attempt to solve:

Simplifying
-15 + x = 0

Solving
-15 + x = 0

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

Add '15' to each side of the equation.
-15 + 15 + x = 0 + 15

Combine like terms: -15 + 15 = 0
0 + x = 0 + 15
x = 0 + 15

Combine like terms: 0 + 15 = 15
x = 15

Simplifying
x = 15

Subproblem 2
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
Solution
x = {15, 1}

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