0=(x+8)(2x-7)

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Solution for 0=(x+8)(2x-7) equation: 


Simplifying
0 = (x + 8)(2x + -7)

Reorder the terms:
0 = (8 + x)(2x + -7)

Reorder the terms:
0 = (8 + x)(-7 + 2x)

Multiply (8 + x) * (-7 + 2x)
0 = (8(-7 + 2x) + x(-7 + 2x))
0 = ((-7 * 8 + 2x * 8) + x(-7 + 2x))
0 = ((-56 + 16x) + x(-7 + 2x))
0 = (-56 + 16x + (-7 * x + 2x * x))
0 = (-56 + 16x + (-7x + 2x2))

Combine like terms: 16x + -7x = 9x
0 = (-56 + 9x + 2x2)

Solving
0 = -56 + 9x + 2x2

Solving for variable 'x'.

Combine like terms: 0 + 56 = 56
56 + -9x + -2x2 = -56 + 9x + 2x2 + 56 + -9x + -2x2

Reorder the terms:
56 + -9x + -2x2 = -56 + 56 + 9x + -9x + 2x2 + -2x2

Combine like terms: -56 + 56 = 0
56 + -9x + -2x2 = 0 + 9x + -9x + 2x2 + -2x2
56 + -9x + -2x2 = 9x + -9x + 2x2 + -2x2

Combine like terms: 9x + -9x = 0
56 + -9x + -2x2 = 0 + 2x2 + -2x2
56 + -9x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
56 + -9x + -2x2 = 0

Factor a trinomial.
(7 + -2x)(8 + x) = 0


Subproblem 1
Set the factor '(7 + -2x)' equal to zero and attempt to solve:

Simplifying
7 + -2x = 0

Solving
7 + -2x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -2x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -2x = 0 + -7
-2x = 0 + -7

Combine like terms: 0 + -7 = -7
-2x = -7

Divide each side by '-2'.
x = 3.5

Simplifying
x = 3.5

Subproblem 2
Set the factor '(8 + x)' equal to zero and attempt to solve:

Simplifying
8 + x = 0

Solving
8 + x = 0

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

Add '-8' to each side of the equation.
8 + -8 + x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + x = 0 + -8
x = 0 + -8

Combine like terms: 0 + -8 = -8
x = -8

Simplifying
x = -8
Solution
x = {3.5, -8}

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