(6x-5)(x+6)=(x-10)(1-4x)

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Solution for (6x-5)(x+6)=(x-10)(1-4x) equation: 


Simplifying
(6x + -5)(x + 6) = (x + -10)(1 + -4x)

Reorder the terms:
(-5 + 6x)(x + 6) = (x + -10)(1 + -4x)

Reorder the terms:
(-5 + 6x)(6 + x) = (x + -10)(1 + -4x)

Multiply (-5 + 6x) * (6 + x)
(-5(6 + x) + 6x * (6 + x)) = (x + -10)(1 + -4x)
((6 * -5 + x * -5) + 6x * (6 + x)) = (x + -10)(1 + -4x)
((-30 + -5x) + 6x * (6 + x)) = (x + -10)(1 + -4x)
(-30 + -5x + (6 * 6x + x * 6x)) = (x + -10)(1 + -4x)
(-30 + -5x + (36x + 6x2)) = (x + -10)(1 + -4x)

Combine like terms: -5x + 36x = 31x
(-30 + 31x + 6x2) = (x + -10)(1 + -4x)

Reorder the terms:
-30 + 31x + 6x2 = (-10 + x)(1 + -4x)

Multiply (-10 + x) * (1 + -4x)
-30 + 31x + 6x2 = (-10(1 + -4x) + x(1 + -4x))
-30 + 31x + 6x2 = ((1 * -10 + -4x * -10) + x(1 + -4x))
-30 + 31x + 6x2 = ((-10 + 40x) + x(1 + -4x))
-30 + 31x + 6x2 = (-10 + 40x + (1 * x + -4x * x))
-30 + 31x + 6x2 = (-10 + 40x + (1x + -4x2))

Combine like terms: 40x + 1x = 41x
-30 + 31x + 6x2 = (-10 + 41x + -4x2)

Solving
-30 + 31x + 6x2 = -10 + 41x + -4x2

Solving for variable 'x'.

Reorder the terms:
-30 + 10 + 31x + -41x + 6x2 + 4x2 = -10 + 41x + -4x2 + 10 + -41x + 4x2

Combine like terms: -30 + 10 = -20
-20 + 31x + -41x + 6x2 + 4x2 = -10 + 41x + -4x2 + 10 + -41x + 4x2

Combine like terms: 31x + -41x = -10x
-20 + -10x + 6x2 + 4x2 = -10 + 41x + -4x2 + 10 + -41x + 4x2

Combine like terms: 6x2 + 4x2 = 10x2
-20 + -10x + 10x2 = -10 + 41x + -4x2 + 10 + -41x + 4x2

Reorder the terms:
-20 + -10x + 10x2 = -10 + 10 + 41x + -41x + -4x2 + 4x2

Combine like terms: -10 + 10 = 0
-20 + -10x + 10x2 = 0 + 41x + -41x + -4x2 + 4x2
-20 + -10x + 10x2 = 41x + -41x + -4x2 + 4x2

Combine like terms: 41x + -41x = 0
-20 + -10x + 10x2 = 0 + -4x2 + 4x2
-20 + -10x + 10x2 = -4x2 + 4x2

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

Factor out the Greatest Common Factor (GCF), '10'.
10(-2 + -1x + x2) = 0

Factor a trinomial.
10((-1 + -1x)(2 + -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 '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

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

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

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-1, 2}

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