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

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

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

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

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

Multiply (6 + -7x) * (-5 + 6x)
(6(-5 + 6x) + -7x * (-5 + 6x)) = 0
((-5 * 6 + 6x * 6) + -7x * (-5 + 6x)) = 0
((-30 + 36x) + -7x * (-5 + 6x)) = 0
(-30 + 36x + (-5 * -7x + 6x * -7x)) = 0
(-30 + 36x + (35x + -42x2)) = 0

Combine like terms: 36x + 35x = 71x
(-30 + 71x + -42x2) = 0

Solving
-30 + 71x + -42x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-6 + 7x)(5 + -6x) = 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 + -6x)' equal to zero and attempt to solve:

Simplifying
5 + -6x = 0

Solving
5 + -6x = 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 + -6x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -6x = 0 + -5
-6x = 0 + -5

Combine like terms: 0 + -5 = -5
-6x = -5

Divide each side by '-6'.
x = 0.8333333333

Simplifying
x = 0.8333333333
Solution
x = {0.8571428571, 0.8333333333}