(2x-1)(x+6)=(x-6)(x+1)

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Solution for (2x-1)(x+6)=(x-6)(x+1) equation: 


Simplifying
(2x + -1)(x + 6) = (x + -6)(x + 1)

Reorder the terms:
(-1 + 2x)(x + 6) = (x + -6)(x + 1)

Reorder the terms:
(-1 + 2x)(6 + x) = (x + -6)(x + 1)

Multiply (-1 + 2x) * (6 + x)
(-1(6 + x) + 2x * (6 + x)) = (x + -6)(x + 1)
((6 * -1 + x * -1) + 2x * (6 + x)) = (x + -6)(x + 1)
((-6 + -1x) + 2x * (6 + x)) = (x + -6)(x + 1)
(-6 + -1x + (6 * 2x + x * 2x)) = (x + -6)(x + 1)
(-6 + -1x + (12x + 2x2)) = (x + -6)(x + 1)

Combine like terms: -1x + 12x = 11x
(-6 + 11x + 2x2) = (x + -6)(x + 1)

Reorder the terms:
-6 + 11x + 2x2 = (-6 + x)(x + 1)

Reorder the terms:
-6 + 11x + 2x2 = (-6 + x)(1 + x)

Multiply (-6 + x) * (1 + x)
-6 + 11x + 2x2 = (-6(1 + x) + x(1 + x))
-6 + 11x + 2x2 = ((1 * -6 + x * -6) + x(1 + x))
-6 + 11x + 2x2 = ((-6 + -6x) + x(1 + x))
-6 + 11x + 2x2 = (-6 + -6x + (1 * x + x * x))
-6 + 11x + 2x2 = (-6 + -6x + (1x + x2))

Combine like terms: -6x + 1x = -5x
-6 + 11x + 2x2 = (-6 + -5x + x2)

Add '6' to each side of the equation.
-6 + 11x + 6 + 2x2 = -6 + -5x + 6 + x2

Reorder the terms:
-6 + 6 + 11x + 2x2 = -6 + -5x + 6 + x2

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

Reorder the terms:
11x + 2x2 = -6 + 6 + -5x + x2

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

Solving
11x + 2x2 = -5x + x2

Solving for variable 'x'.

Reorder the terms:
11x + 5x + 2x2 + -1x2 = -5x + x2 + 5x + -1x2

Combine like terms: 11x + 5x = 16x
16x + 2x2 + -1x2 = -5x + x2 + 5x + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
16x + 1x2 = -5x + x2 + 5x + -1x2

Reorder the terms:
16x + 1x2 = -5x + 5x + x2 + -1x2

Combine like terms: -5x + 5x = 0
16x + 1x2 = 0 + x2 + -1x2
16x + 1x2 = x2 + -1x2

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

Factor out the Greatest Common Factor (GCF), 'x'.
x(16 + 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 '(16 + x)' equal to zero and attempt to solve:

Simplifying
16 + x = 0

Solving
16 + x = 0

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

Add '-16' to each side of the equation.
16 + -16 + x = 0 + -16

Combine like terms: 16 + -16 = 0
0 + x = 0 + -16
x = 0 + -16

Combine like terms: 0 + -16 = -16
x = -16

Simplifying
x = -16
Solution
x = {0, -16}

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