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

Solution for 0=3(x-5)(x+4) equation:

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

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

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

Multiply (-5 + x) * (4 + x)
0 = 3(-5(4 + x) + x(4 + x))
0 = 3((4 * -5 + x * -5) + x(4 + x))
0 = 3((-20 + -5x) + x(4 + x))
0 = 3(-20 + -5x + (4 * x + x * x))
0 = 3(-20 + -5x + (4x + x2))

Combine like terms: -5x + 4x = -1x
0 = 3(-20 + -1x + x2)
0 = (-20 * 3 + -1x * 3 + x2 * 3)
0 = (-60 + -3x + 3x2)

Solving
0 = -60 + -3x + 3x2

Solving for variable 'x'.

Combine like terms: 0 + 60 = 60
60 + 3x + -3x2 = -60 + -3x + 3x2 + 60 + 3x + -3x2

Reorder the terms:
60 + 3x + -3x2 = -60 + 60 + -3x + 3x + 3x2 + -3x2

Combine like terms: -60 + 60 = 0
60 + 3x + -3x2 = 0 + -3x + 3x + 3x2 + -3x2
60 + 3x + -3x2 = -3x + 3x + 3x2 + -3x2

Combine like terms: -3x + 3x = 0
60 + 3x + -3x2 = 0 + 3x2 + -3x2
60 + 3x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
60 + 3x + -3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(20 + x + -1x2) = 0

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

Ignore the factor 3.
Subproblem 1
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 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 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Subproblem 2
Set the factor '(4 + x)' equal to zero and attempt to solve:

Simplifying
4 + x = 0

Solving
4 + x = 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 + x = 0 + -4

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

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

Simplifying
x = -4
Solution
x = {5, -4}