(5x+1)(8+x)=0

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Solution for (5x+1)(8+x)=0 equation: 


Simplifying
(5x + 1)(8 + x) = 0

Reorder the terms:
(1 + 5x)(8 + x) = 0

Multiply (1 + 5x) * (8 + x)
(1(8 + x) + 5x * (8 + x)) = 0
((8 * 1 + x * 1) + 5x * (8 + x)) = 0
((8 + 1x) + 5x * (8 + x)) = 0
(8 + 1x + (8 * 5x + x * 5x)) = 0
(8 + 1x + (40x + 5x2)) = 0

Combine like terms: 1x + 40x = 41x
(8 + 41x + 5x2) = 0

Solving
8 + 41x + 5x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(8 + x)(1 + 5x) = 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 '(1 + 5x)' equal to zero and attempt to solve:

Simplifying
1 + 5x = 0

Solving
1 + 5x = 0

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

Add '-1' to each side of the equation.
1 + -1 + 5x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 5x = 0 + -1
5x = 0 + -1

Combine like terms: 0 + -1 = -1
5x = -1

Divide each side by '5'.
x = -0.2

Simplifying
x = -0.2
Solution
x = {-8, -0.2}

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