(7x+3)(4x-12)=0

Solution for (7x+3)(4x-12)=0 equation:

Simplifying
(7x + 3)(4x + -12) = 0

Reorder the terms:
(3 + 7x)(4x + -12) = 0

Reorder the terms:
(3 + 7x)(-12 + 4x) = 0

Multiply (3 + 7x) * (-12 + 4x)
(3(-12 + 4x) + 7x * (-12 + 4x)) = 0
((-12 * 3 + 4x * 3) + 7x * (-12 + 4x)) = 0
((-36 + 12x) + 7x * (-12 + 4x)) = 0
(-36 + 12x + (-12 * 7x + 4x * 7x)) = 0
(-36 + 12x + (-84x + 28x2)) = 0

Combine like terms: 12x + -84x = -72x
(-36 + -72x + 28x2) = 0

Solving
-36 + -72x + 28x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-9 + -18x + 7x2) = 0

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

Ignore the factor 4.
Subproblem 1
Set the factor '(-3 + -7x)' equal to zero and attempt to solve:

Simplifying
-3 + -7x = 0

Solving
-3 + -7x = 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 + -7x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -7x = 0 + 3
-7x = 0 + 3

Combine like terms: 0 + 3 = 3
-7x = 3

Divide each side by '-7'.
x = -0.4285714286

Simplifying
x = -0.4285714286
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 = {-0.4285714286, 3}