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

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


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

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

Multiply (8 + 5x) * (7 + x)
(8(7 + x) + 5x * (7 + x)) = 0
((7 * 8 + x * 8) + 5x * (7 + x)) = 0
((56 + 8x) + 5x * (7 + x)) = 0
(56 + 8x + (7 * 5x + x * 5x)) = 0
(56 + 8x + (35x + 5x2)) = 0

Combine like terms: 8x + 35x = 43x
(56 + 43x + 5x2) = 0

Solving
56 + 43x + 5x2 = 0

Solving for variable 'x'.

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


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

Simplifying
7 + x = 0

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

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

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

Simplifying
x = -7

Subproblem 2
Set the factor '(8 + 5x)' equal to zero and attempt to solve:

Simplifying
8 + 5x = 0

Solving
8 + 5x = 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 + 5x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + 5x = 0 + -8
5x = 0 + -8

Combine like terms: 0 + -8 = -8
5x = -8

Divide each side by '5'.
x = -1.6

Simplifying
x = -1.6
Solution
x = {-7, -1.6}

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