(5x-8)(x+6)=0

Solution for (5x-8)(x+6)=0 equation:

Simplifying
(5x + -8)(x + 6) = 0

Reorder the terms:
(-8 + 5x)(x + 6) = 0

Reorder the terms:
(-8 + 5x)(6 + x) = 0

Multiply (-8 + 5x) * (6 + x)
(-8(6 + x) + 5x * (6 + x)) = 0
((6 * -8 + x * -8) + 5x * (6 + x)) = 0
((-48 + -8x) + 5x * (6 + x)) = 0
(-48 + -8x + (6 * 5x + x * 5x)) = 0
(-48 + -8x + (30x + 5x2)) = 0

Combine like terms: -8x + 30x = 22x
(-48 + 22x + 5x2) = 0

Solving
-48 + 22x + 5x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-6 + -1x)(8 + -5x) = 0

Subproblem 1
Set the factor '(-6 + -1x)' equal to zero and attempt to solve:

Simplifying
-6 + -1x = 0

Solving
-6 + -1x = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1x = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1x = 0 + 6
-1x = 0 + 6

Combine like terms: 0 + 6 = 6
-1x = 6

Divide each side by '-1'.
x = -6

Simplifying
x = -6
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 = {-6, 1.6}