(7x-6)(3x+6)=0

Solution for (7x-6)(3x+6)=0 equation:

Simplifying
(7x + -6)(3x + 6) = 0

Reorder the terms:
(-6 + 7x)(3x + 6) = 0

Reorder the terms:
(-6 + 7x)(6 + 3x) = 0

Multiply (-6 + 7x) * (6 + 3x)
(-6(6 + 3x) + 7x * (6 + 3x)) = 0
((6 * -6 + 3x * -6) + 7x * (6 + 3x)) = 0
((-36 + -18x) + 7x * (6 + 3x)) = 0
(-36 + -18x + (6 * 7x + 3x * 7x)) = 0
(-36 + -18x + (42x + 21x2)) = 0

Combine like terms: -18x + 42x = 24x
(-36 + 24x + 21x2) = 0

Solving
-36 + 24x + 21x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-12 + 8x + 7x2) = 0

Factor a trinomial.
3((-2 + -1x)(6 + -7x)) = 0

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

Simplifying
-2 + -1x = 0

Solving
-2 + -1x = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1x = 0 + 2
-1x = 0 + 2

Combine like terms: 0 + 2 = 2
-1x = 2

Divide each side by '-1'.
x = -2

Simplifying
x = -2
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 = {-2, 0.8571428571}