5(3x-2)(x-6)=0

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Solution for 5(3x-2)(x-6)=0 equation: 


Simplifying
5(3x + -2)(x + -6) = 0

Reorder the terms:
5(-2 + 3x)(x + -6) = 0

Reorder the terms:
5(-2 + 3x)(-6 + x) = 0

Multiply (-2 + 3x) * (-6 + x)
5(-2(-6 + x) + 3x * (-6 + x)) = 0
5((-6 * -2 + x * -2) + 3x * (-6 + x)) = 0
5((12 + -2x) + 3x * (-6 + x)) = 0
5(12 + -2x + (-6 * 3x + x * 3x)) = 0
5(12 + -2x + (-18x + 3x2)) = 0

Combine like terms: -2x + -18x = -20x
5(12 + -20x + 3x2) = 0
(12 * 5 + -20x * 5 + 3x2 * 5) = 0
(60 + -100x + 15x2) = 0

Solving
60 + -100x + 15x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(12 + -20x + 3x2) = 0

Factor a trinomial.
5((2 + -3x)(6 + -1x)) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(2 + -3x)' equal to zero and attempt to solve:

Simplifying
2 + -3x = 0

Solving
2 + -3x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + -2 + -3x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3x = 0 + -2
-3x = 0 + -2

Combine like terms: 0 + -2 = -2
-3x = -2

Divide each side by '-3'.
x = 0.6666666667

Simplifying
x = 0.6666666667

Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {0.6666666667, 6}

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