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

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


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

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

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

Multiply (-5 + 4x) * (5 + 3x)
6(-5(5 + 3x) + 4x * (5 + 3x)) = 0
6((5 * -5 + 3x * -5) + 4x * (5 + 3x)) = 0
6((-25 + -15x) + 4x * (5 + 3x)) = 0
6(-25 + -15x + (5 * 4x + 3x * 4x)) = 0
6(-25 + -15x + (20x + 12x2)) = 0

Combine like terms: -15x + 20x = 5x
6(-25 + 5x + 12x2) = 0
(-25 * 6 + 5x * 6 + 12x2 * 6) = 0
(-150 + 30x + 72x2) = 0

Solving
-150 + 30x + 72x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-25 + 5x + 12x2) = 0

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

Ignore the factor 6.

Subproblem 1
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

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 = {-1.666666667, 1.25}

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