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

Solution for 6(4x-5)(3x+4)=0 equation:

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

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

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

Multiply (-5 + 4x) * (4 + 3x)
6(-5(4 + 3x) + 4x * (4 + 3x)) = 0
6((4 * -5 + 3x * -5) + 4x * (4 + 3x)) = 0
6((-20 + -15x) + 4x * (4 + 3x)) = 0
6(-20 + -15x + (4 * 4x + 3x * 4x)) = 0
6(-20 + -15x + (16x + 12x2)) = 0

Combine like terms: -15x + 16x = 1x
6(-20 + 1x + 12x2) = 0
(-20 * 6 + 1x * 6 + 12x2 * 6) = 0
(-120 + 6x + 72x2) = 0

Solving
-120 + 6x + 72x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-20 + x + 12x2) = 0

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

Ignore the factor 6.
Subproblem 1
Set the factor '(-4 + -3x)' equal to zero and attempt to solve:

Simplifying
-4 + -3x = 0

Solving
-4 + -3x = 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 + -3x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -3x = 0 + 4
-3x = 0 + 4

Combine like terms: 0 + 4 = 4
-3x = 4

Divide each side by '-3'.
x = -1.333333333

Simplifying
x = -1.333333333
Subproblem 2
Set the factor '(5 + -4x)' equal to zero and attempt to solve:

Simplifying
5 + -4x = 0

Solving
5 + -4x = 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 + -4x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -4x = 0 + -5
-4x = 0 + -5

Combine like terms: 0 + -5 = -5
-4x = -5

Divide each side by '-4'.
x = 1.25

Simplifying
x = 1.25
Solution
x = {-1.333333333, 1.25}