(8x-5)(6-7x)=0

Solution for (8x-5)(6-7x)=0 equation:

Simplifying
(8x + -5)(6 + -7x) = 0

Reorder the terms:
(-5 + 8x)(6 + -7x) = 0

Multiply (-5 + 8x) * (6 + -7x)
(-5(6 + -7x) + 8x * (6 + -7x)) = 0
((6 * -5 + -7x * -5) + 8x * (6 + -7x)) = 0
((-30 + 35x) + 8x * (6 + -7x)) = 0
(-30 + 35x + (6 * 8x + -7x * 8x)) = 0
(-30 + 35x + (48x + -56x2)) = 0

Combine like terms: 35x + 48x = 83x
(-30 + 83x + -56x2) = 0

Solving
-30 + 83x + -56x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-6 + 7x)(5 + -8x) = 0

Subproblem 1
Set the factor '(-6 + 7x)' equal to zero and attempt to solve:

Simplifying
-6 + 7x = 0

Solving
-6 + 7x = 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 + 7x = 0 + 6

Combine like terms: -6 + 6 = 0
0 + 7x = 0 + 6
7x = 0 + 6

Combine like terms: 0 + 6 = 6
7x = 6

Divide each side by '7'.
x = 0.8571428571

Simplifying
x = 0.8571428571
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 = {0.8571428571, 0.625}