6(5x-4)(3x-12)=0

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Solution for 6(5x-4)(3x-12)=0 equation: 


Simplifying
6(5x + -4)(3x + -12) = 0

Reorder the terms:
6(-4 + 5x)(3x + -12) = 0

Reorder the terms:
6(-4 + 5x)(-12 + 3x) = 0

Multiply (-4 + 5x) * (-12 + 3x)
6(-4(-12 + 3x) + 5x * (-12 + 3x)) = 0
6((-12 * -4 + 3x * -4) + 5x * (-12 + 3x)) = 0
6((48 + -12x) + 5x * (-12 + 3x)) = 0
6(48 + -12x + (-12 * 5x + 3x * 5x)) = 0
6(48 + -12x + (-60x + 15x2)) = 0

Combine like terms: -12x + -60x = -72x
6(48 + -72x + 15x2) = 0
(48 * 6 + -72x * 6 + 15x2 * 6) = 0
(288 + -432x + 90x2) = 0

Solving
288 + -432x + 90x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '18'.
18(16 + -24x + 5x2) = 0

Factor a trinomial.
18((4 + -5x)(4 + -1x)) = 0

Ignore the factor 18.

Subproblem 1
Set the factor '(4 + -5x)' equal to zero and attempt to solve:

Simplifying
4 + -5x = 0

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

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

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

Divide each side by '-5'.
x = 0.8

Simplifying
x = 0.8

Subproblem 2
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
Solution
x = {0.8, 4}

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