(6x-7)(x-8)=(x+40)(1-2x)

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Solution for (6x-7)(x-8)=(x+40)(1-2x) equation: 


Simplifying
(6x + -7)(x + -8) = (x + 40)(1 + -2x)

Reorder the terms:
(-7 + 6x)(x + -8) = (x + 40)(1 + -2x)

Reorder the terms:
(-7 + 6x)(-8 + x) = (x + 40)(1 + -2x)

Multiply (-7 + 6x) * (-8 + x)
(-7(-8 + x) + 6x * (-8 + x)) = (x + 40)(1 + -2x)
((-8 * -7 + x * -7) + 6x * (-8 + x)) = (x + 40)(1 + -2x)
((56 + -7x) + 6x * (-8 + x)) = (x + 40)(1 + -2x)
(56 + -7x + (-8 * 6x + x * 6x)) = (x + 40)(1 + -2x)
(56 + -7x + (-48x + 6x2)) = (x + 40)(1 + -2x)

Combine like terms: -7x + -48x = -55x
(56 + -55x + 6x2) = (x + 40)(1 + -2x)

Reorder the terms:
56 + -55x + 6x2 = (40 + x)(1 + -2x)

Multiply (40 + x) * (1 + -2x)
56 + -55x + 6x2 = (40(1 + -2x) + x(1 + -2x))
56 + -55x + 6x2 = ((1 * 40 + -2x * 40) + x(1 + -2x))
56 + -55x + 6x2 = ((40 + -80x) + x(1 + -2x))
56 + -55x + 6x2 = (40 + -80x + (1 * x + -2x * x))
56 + -55x + 6x2 = (40 + -80x + (1x + -2x2))

Combine like terms: -80x + 1x = -79x
56 + -55x + 6x2 = (40 + -79x + -2x2)

Solving
56 + -55x + 6x2 = 40 + -79x + -2x2

Solving for variable 'x'.

Reorder the terms:
56 + -40 + -55x + 79x + 6x2 + 2x2 = 40 + -79x + -2x2 + -40 + 79x + 2x2

Combine like terms: 56 + -40 = 16
16 + -55x + 79x + 6x2 + 2x2 = 40 + -79x + -2x2 + -40 + 79x + 2x2

Combine like terms: -55x + 79x = 24x
16 + 24x + 6x2 + 2x2 = 40 + -79x + -2x2 + -40 + 79x + 2x2

Combine like terms: 6x2 + 2x2 = 8x2
16 + 24x + 8x2 = 40 + -79x + -2x2 + -40 + 79x + 2x2

Reorder the terms:
16 + 24x + 8x2 = 40 + -40 + -79x + 79x + -2x2 + 2x2

Combine like terms: 40 + -40 = 0
16 + 24x + 8x2 = 0 + -79x + 79x + -2x2 + 2x2
16 + 24x + 8x2 = -79x + 79x + -2x2 + 2x2

Combine like terms: -79x + 79x = 0
16 + 24x + 8x2 = 0 + -2x2 + 2x2
16 + 24x + 8x2 = -2x2 + 2x2

Combine like terms: -2x2 + 2x2 = 0
16 + 24x + 8x2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(2 + 3x + x2) = 0

Factor a trinomial.
8((2 + x)(1 + x)) = 0

Ignore the factor 8.

Subproblem 1
Set the factor '(2 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

Solving
2 + x = 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 + x = 0 + -2

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

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

Simplifying
x = -2

Subproblem 2
Set the factor '(1 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

Solving
1 + x = 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 + x = 0 + -1

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

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

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

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