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

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

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

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

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

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

Combine like terms: -5x + 8x = 3x
(-5 + 3x + 8x2) = 0

Solving
-5 + 3x + 8x2 = 0

Solving for variable 'x'.

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

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

Simplifying
-1 + -1x = 0

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

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

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

Divide each side by '-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}