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

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

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

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

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

Multiply (-6 + 7x) * (6 + 8x)
(-6(6 + 8x) + 7x * (6 + 8x)) = 0
((6 * -6 + 8x * -6) + 7x * (6 + 8x)) = 0
((-36 + -48x) + 7x * (6 + 8x)) = 0
(-36 + -48x + (6 * 7x + 8x * 7x)) = 0
(-36 + -48x + (42x + 56x2)) = 0

Combine like terms: -48x + 42x = -6x
(-36 + -6x + 56x2) = 0

Solving
-36 + -6x + 56x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-18 + -3x + 28x2) = 0

Factor a trinomial.
2((-3 + -4x)(6 + -7x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-3 + -4x)' equal to zero and attempt to solve:

Simplifying
-3 + -4x = 0

Solving
-3 + -4x = 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 + -4x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -4x = 0 + 3
-4x = 0 + 3

Combine like terms: 0 + 3 = 3
-4x = 3

Divide each side by '-4'.
x = -0.75

Simplifying
x = -0.75
Subproblem 2
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
Solution
x = {-0.75, 0.8571428571}