(4x+5)(8+x)=0

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Solution for (4x+5)(8+x)=0 equation: 


Simplifying
(4x + 5)(8 + x) = 0

Reorder the terms:
(5 + 4x)(8 + x) = 0

Multiply (5 + 4x) * (8 + x)
(5(8 + x) + 4x * (8 + x)) = 0
((8 * 5 + x * 5) + 4x * (8 + x)) = 0
((40 + 5x) + 4x * (8 + x)) = 0
(40 + 5x + (8 * 4x + x * 4x)) = 0
(40 + 5x + (32x + 4x2)) = 0

Combine like terms: 5x + 32x = 37x
(40 + 37x + 4x2) = 0

Solving
40 + 37x + 4x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(8 + x)(5 + 4x) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(5 + 4x)' equal to zero and attempt to solve:

Simplifying
5 + 4x = 0

Solving
5 + 4x = 0

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

Add '-5' to each side of the equation.
5 + -5 + 4x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 4x = 0 + -5
4x = 0 + -5

Combine like terms: 0 + -5 = -5
4x = -5

Divide each side by '4'.
x = -1.25

Simplifying
x = -1.25
Solution
x = {-8, -1.25}

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