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

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

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

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

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

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

Combine like terms: 4x + -3x = 1x
3(-12 + 1x + x2) = 0
(-12 * 3 + 1x * 3 + x2 * 3) = 0
(-36 + 3x + 3x2) = 0

Solving
-36 + 3x + 3x2 = 0

Solving for variable 'x'.

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

Factor a trinomial.
3((-4 + -1x)(3 + -1x)) = 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 + -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 = {-4, 3}