(4x-12)(7x+6)=0

Solution for (4x-12)(7x+6)=0 equation:

Simplifying
(4x + -12)(7x + 6) = 0

Reorder the terms:
(-12 + 4x)(7x + 6) = 0

Reorder the terms:
(-12 + 4x)(6 + 7x) = 0

Multiply (-12 + 4x) * (6 + 7x)
(-12(6 + 7x) + 4x * (6 + 7x)) = 0
((6 * -12 + 7x * -12) + 4x * (6 + 7x)) = 0
((-72 + -84x) + 4x * (6 + 7x)) = 0
(-72 + -84x + (6 * 4x + 7x * 4x)) = 0
(-72 + -84x + (24x + 28x2)) = 0

Combine like terms: -84x + 24x = -60x
(-72 + -60x + 28x2) = 0

Solving
-72 + -60x + 28x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-18 + -15x + 7x2) = 0

Factor a trinomial.
4((-6 + -7x)(3 + -1x)) = 0

Ignore the factor 4.
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 '(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 = {-0.8571428571, 3}