4(x+6)(3x-5)=

Solution for 4(x+6)(3x-5)= equation:

Simplifying
4(x + 6)(3x + -5) = 0

Reorder the terms:
4(6 + x)(3x + -5) = 0

Reorder the terms:
4(6 + x)(-5 + 3x) = 0

Multiply (6 + x) * (-5 + 3x)
4(6(-5 + 3x) + x(-5 + 3x)) = 0
4((-5 * 6 + 3x * 6) + x(-5 + 3x)) = 0
4((-30 + 18x) + x(-5 + 3x)) = 0
4(-30 + 18x + (-5 * x + 3x * x)) = 0
4(-30 + 18x + (-5x + 3x2)) = 0

Combine like terms: 18x + -5x = 13x
4(-30 + 13x + 3x2) = 0
(-30 * 4 + 13x * 4 + 3x2 * 4) = 0
(-120 + 52x + 12x2) = 0

Solving
-120 + 52x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-30 + 13x + 3x2) = 0

Factor a trinomial.
4((-6 + -1x)(5 + -3x)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-6 + -1x)' equal to zero and attempt to solve:

Simplifying
-6 + -1x = 0

Solving
-6 + -1x = 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 + -1x = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1x = 0 + 6
-1x = 0 + 6

Combine like terms: 0 + 6 = 6
-1x = 6

Divide each side by '-1'.
x = -6

Simplifying
x = -6
Subproblem 2
Set the factor '(5 + -3x)' equal to zero and attempt to solve:

Simplifying
5 + -3x = 0

Solving
5 + -3x = 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 + -3x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -3x = 0 + -5
-3x = 0 + -5

Combine like terms: 0 + -5 = -5
-3x = -5

Divide each side by '-3'.
x = 1.666666667

Simplifying
x = 1.666666667
Solution
x = {-6, 1.666666667}