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

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


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

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

Multiply (8 + 5x) * (4 + x)
(8(4 + x) + 5x * (4 + x)) = 0
((4 * 8 + x * 8) + 5x * (4 + x)) = 0
((32 + 8x) + 5x * (4 + x)) = 0
(32 + 8x + (4 * 5x + x * 5x)) = 0
(32 + 8x + (20x + 5x2)) = 0

Combine like terms: 8x + 20x = 28x
(32 + 28x + 5x2) = 0

Solving
32 + 28x + 5x2 = 0

Solving for variable 'x'.

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


Subproblem 1
Set the factor '(4 + x)' equal to zero and attempt to solve:

Simplifying
4 + x = 0

Solving
4 + x = 0

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

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

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

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

Simplifying
x = -4

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 = {-4, -1.6}

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