(5x-7)(8+x)=0

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Solution for (5x-7)(8+x)=0 equation: 


Simplifying
(5x + -7)(8 + x) = 0

Reorder the terms:
(-7 + 5x)(8 + x) = 0

Multiply (-7 + 5x) * (8 + x)
(-7(8 + x) + 5x * (8 + x)) = 0
((8 * -7 + x * -7) + 5x * (8 + x)) = 0
((-56 + -7x) + 5x * (8 + x)) = 0
(-56 + -7x + (8 * 5x + x * 5x)) = 0
(-56 + -7x + (40x + 5x2)) = 0

Combine like terms: -7x + 40x = 33x
(-56 + 33x + 5x2) = 0

Solving
-56 + 33x + 5x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-8 + -1x)(7 + -5x) = 0


Subproblem 1
Set the factor '(-8 + -1x)' equal to zero and attempt to solve:

Simplifying
-8 + -1x = 0

Solving
-8 + -1x = 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 + -1x = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1x = 0 + 8
-1x = 0 + 8

Combine like terms: 0 + 8 = 8
-1x = 8

Divide each side by '-1'.
x = -8

Simplifying
x = -8

Subproblem 2
Set the factor '(7 + -5x)' equal to zero and attempt to solve:

Simplifying
7 + -5x = 0

Solving
7 + -5x = 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 + -5x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -5x = 0 + -7
-5x = 0 + -7

Combine like terms: 0 + -7 = -7
-5x = -7

Divide each side by '-5'.
x = 1.4

Simplifying
x = 1.4
Solution
x = {-8, 1.4}

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