3(2x-3)(x+4)=0

Solution for 3(2x-3)(x+4)=0 equation:

Simplifying
3(2x + -3)(x + 4) = 0

Reorder the terms:
3(-3 + 2x)(x + 4) = 0

Reorder the terms:
3(-3 + 2x)(4 + x) = 0

Multiply (-3 + 2x) * (4 + x)
3(-3(4 + x) + 2x * (4 + x)) = 0
3((4 * -3 + x * -3) + 2x * (4 + x)) = 0
3((-12 + -3x) + 2x * (4 + x)) = 0
3(-12 + -3x + (4 * 2x + x * 2x)) = 0
3(-12 + -3x + (8x + 2x2)) = 0

Combine like terms: -3x + 8x = 5x
3(-12 + 5x + 2x2) = 0
(-12 * 3 + 5x * 3 + 2x2 * 3) = 0
(-36 + 15x + 6x2) = 0

Solving
-36 + 15x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-12 + 5x + 2x2) = 0

Factor a trinomial.
3((-4 + -1x)(3 + -2x)) = 0

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

Simplifying
-4 + -1x = 0

Solving
-4 + -1x = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1x = 0 + 4
-1x = 0 + 4

Combine like terms: 0 + 4 = 4
-1x = 4

Divide each side by '-1'.
x = -4

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

Simplifying
3 + -2x = 0

Solving
3 + -2x = 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 + -2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2x = 0 + -3
-2x = 0 + -3

Combine like terms: 0 + -3 = -3
-2x = -3

Divide each side by '-2'.
x = 1.5

Simplifying
x = 1.5
Solution
x = {-4, 1.5}