(2x-6)(8x+5)=0

Solution for (2x-6)(8x+5)=0 equation:

Simplifying
(2x + -6)(8x + 5) = 0

Reorder the terms:
(-6 + 2x)(8x + 5) = 0

Reorder the terms:
(-6 + 2x)(5 + 8x) = 0

Multiply (-6 + 2x) * (5 + 8x)
(-6(5 + 8x) + 2x * (5 + 8x)) = 0
((5 * -6 + 8x * -6) + 2x * (5 + 8x)) = 0
((-30 + -48x) + 2x * (5 + 8x)) = 0
(-30 + -48x + (5 * 2x + 8x * 2x)) = 0
(-30 + -48x + (10x + 16x2)) = 0

Combine like terms: -48x + 10x = -38x
(-30 + -38x + 16x2) = 0

Solving
-30 + -38x + 16x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-15 + -19x + 8x2) = 0

Factor a trinomial.
2((-5 + -8x)(3 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
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
Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-0.625, 3}