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

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


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

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

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

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

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

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

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

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

Combine like terms: 7x + 32x = 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.
(6 + -1x)(2 + x) = 0


Subproblem 1
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 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 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6

Subproblem 2
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
Solution
x = {6, -2}

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