(x+6)(6x-7)=(x-12)(1-4x)

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Solution for (x+6)(6x-7)=(x-12)(1-4x) equation: 


Simplifying
(x + 6)(6x + -7) = (x + -12)(1 + -4x)

Reorder the terms:
(6 + x)(6x + -7) = (x + -12)(1 + -4x)

Reorder the terms:
(6 + x)(-7 + 6x) = (x + -12)(1 + -4x)

Multiply (6 + x) * (-7 + 6x)
(6(-7 + 6x) + x(-7 + 6x)) = (x + -12)(1 + -4x)
((-7 * 6 + 6x * 6) + x(-7 + 6x)) = (x + -12)(1 + -4x)
((-42 + 36x) + x(-7 + 6x)) = (x + -12)(1 + -4x)
(-42 + 36x + (-7 * x + 6x * x)) = (x + -12)(1 + -4x)
(-42 + 36x + (-7x + 6x2)) = (x + -12)(1 + -4x)

Combine like terms: 36x + -7x = 29x
(-42 + 29x + 6x2) = (x + -12)(1 + -4x)

Reorder the terms:
-42 + 29x + 6x2 = (-12 + x)(1 + -4x)

Multiply (-12 + x) * (1 + -4x)
-42 + 29x + 6x2 = (-12(1 + -4x) + x(1 + -4x))
-42 + 29x + 6x2 = ((1 * -12 + -4x * -12) + x(1 + -4x))
-42 + 29x + 6x2 = ((-12 + 48x) + x(1 + -4x))
-42 + 29x + 6x2 = (-12 + 48x + (1 * x + -4x * x))
-42 + 29x + 6x2 = (-12 + 48x + (1x + -4x2))

Combine like terms: 48x + 1x = 49x
-42 + 29x + 6x2 = (-12 + 49x + -4x2)

Solving
-42 + 29x + 6x2 = -12 + 49x + -4x2

Solving for variable 'x'.

Reorder the terms:
-42 + 12 + 29x + -49x + 6x2 + 4x2 = -12 + 49x + -4x2 + 12 + -49x + 4x2

Combine like terms: -42 + 12 = -30
-30 + 29x + -49x + 6x2 + 4x2 = -12 + 49x + -4x2 + 12 + -49x + 4x2

Combine like terms: 29x + -49x = -20x
-30 + -20x + 6x2 + 4x2 = -12 + 49x + -4x2 + 12 + -49x + 4x2

Combine like terms: 6x2 + 4x2 = 10x2
-30 + -20x + 10x2 = -12 + 49x + -4x2 + 12 + -49x + 4x2

Reorder the terms:
-30 + -20x + 10x2 = -12 + 12 + 49x + -49x + -4x2 + 4x2

Combine like terms: -12 + 12 = 0
-30 + -20x + 10x2 = 0 + 49x + -49x + -4x2 + 4x2
-30 + -20x + 10x2 = 49x + -49x + -4x2 + 4x2

Combine like terms: 49x + -49x = 0
-30 + -20x + 10x2 = 0 + -4x2 + 4x2
-30 + -20x + 10x2 = -4x2 + 4x2

Combine like terms: -4x2 + 4x2 = 0
-30 + -20x + 10x2 = 0

Factor out the Greatest Common Factor (GCF), '10'.
10(-3 + -2x + x2) = 0

Factor a trinomial.
10((-1 + -1x)(3 + -1x)) = 0

Ignore the factor 10.

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}

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