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

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

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

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

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

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

Combine like terms: 8x + 5x = 13x
(5 + 13x + 8x2) = 0

Solving
5 + 13x + 8x2 = 0

Solving for variable 'x'.

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

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

Simplifying
1 + x = 0

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

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

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

Simplifying
x = -1
Subproblem 2
Set the factor '(5 + 8x)' equal to zero and attempt to solve:

Simplifying
5 + 8x = 0

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

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

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

Divide each side by '8'.
x = -0.625

Simplifying
x = -0.625
Solution
x = {-1, -0.625}