(7x-8)(x-5)=(x-4)(8x-7)

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Solution for (7x-8)(x-5)=(x-4)(8x-7) equation: 


Simplifying
(7x + -8)(x + -5) = (x + -4)(8x + -7)

Reorder the terms:
(-8 + 7x)(x + -5) = (x + -4)(8x + -7)

Reorder the terms:
(-8 + 7x)(-5 + x) = (x + -4)(8x + -7)

Multiply (-8 + 7x) * (-5 + x)
(-8(-5 + x) + 7x * (-5 + x)) = (x + -4)(8x + -7)
((-5 * -8 + x * -8) + 7x * (-5 + x)) = (x + -4)(8x + -7)
((40 + -8x) + 7x * (-5 + x)) = (x + -4)(8x + -7)
(40 + -8x + (-5 * 7x + x * 7x)) = (x + -4)(8x + -7)
(40 + -8x + (-35x + 7x2)) = (x + -4)(8x + -7)

Combine like terms: -8x + -35x = -43x
(40 + -43x + 7x2) = (x + -4)(8x + -7)

Reorder the terms:
40 + -43x + 7x2 = (-4 + x)(8x + -7)

Reorder the terms:
40 + -43x + 7x2 = (-4 + x)(-7 + 8x)

Multiply (-4 + x) * (-7 + 8x)
40 + -43x + 7x2 = (-4(-7 + 8x) + x(-7 + 8x))
40 + -43x + 7x2 = ((-7 * -4 + 8x * -4) + x(-7 + 8x))
40 + -43x + 7x2 = ((28 + -32x) + x(-7 + 8x))
40 + -43x + 7x2 = (28 + -32x + (-7 * x + 8x * x))
40 + -43x + 7x2 = (28 + -32x + (-7x + 8x2))

Combine like terms: -32x + -7x = -39x
40 + -43x + 7x2 = (28 + -39x + 8x2)

Solving
40 + -43x + 7x2 = 28 + -39x + 8x2

Solving for variable 'x'.

Reorder the terms:
40 + -28 + -43x + 39x + 7x2 + -8x2 = 28 + -39x + 8x2 + -28 + 39x + -8x2

Combine like terms: 40 + -28 = 12
12 + -43x + 39x + 7x2 + -8x2 = 28 + -39x + 8x2 + -28 + 39x + -8x2

Combine like terms: -43x + 39x = -4x
12 + -4x + 7x2 + -8x2 = 28 + -39x + 8x2 + -28 + 39x + -8x2

Combine like terms: 7x2 + -8x2 = -1x2
12 + -4x + -1x2 = 28 + -39x + 8x2 + -28 + 39x + -8x2

Reorder the terms:
12 + -4x + -1x2 = 28 + -28 + -39x + 39x + 8x2 + -8x2

Combine like terms: 28 + -28 = 0
12 + -4x + -1x2 = 0 + -39x + 39x + 8x2 + -8x2
12 + -4x + -1x2 = -39x + 39x + 8x2 + -8x2

Combine like terms: -39x + 39x = 0
12 + -4x + -1x2 = 0 + 8x2 + -8x2
12 + -4x + -1x2 = 8x2 + -8x2

Combine like terms: 8x2 + -8x2 = 0
12 + -4x + -1x2 = 0

Factor a trinomial.
(2 + -1x)(6 + x) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(6 + x)' equal to zero and attempt to solve:

Simplifying
6 + x = 0

Solving
6 + x = 0

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

Add '-6' to each side of the equation.
6 + -6 + x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + x = 0 + -6
x = 0 + -6

Combine like terms: 0 + -6 = -6
x = -6

Simplifying
x = -6
Solution
x = {2, -6}

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