5(6x-5)(2x-1)=0

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Solution for 5(6x-5)(2x-1)=0 equation: 


Simplifying
5(6x + -5)(2x + -1) = 0

Reorder the terms:
5(-5 + 6x)(2x + -1) = 0

Reorder the terms:
5(-5 + 6x)(-1 + 2x) = 0

Multiply (-5 + 6x) * (-1 + 2x)
5(-5(-1 + 2x) + 6x * (-1 + 2x)) = 0
5((-1 * -5 + 2x * -5) + 6x * (-1 + 2x)) = 0
5((5 + -10x) + 6x * (-1 + 2x)) = 0
5(5 + -10x + (-1 * 6x + 2x * 6x)) = 0
5(5 + -10x + (-6x + 12x2)) = 0

Combine like terms: -10x + -6x = -16x
5(5 + -16x + 12x2) = 0
(5 * 5 + -16x * 5 + 12x2 * 5) = 0
(25 + -80x + 60x2) = 0

Solving
25 + -80x + 60x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(5 + -16x + 12x2) = 0

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

Ignore the factor 5.

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

Simplifying
1 + -2x = 0

Solving
1 + -2x = 0

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

Add '-1' to each side of the equation.
1 + -1 + -2x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2x = 0 + -1
-2x = 0 + -1

Combine like terms: 0 + -1 = -1
-2x = -1

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5

Subproblem 2
Set the factor '(5 + -6x)' equal to zero and attempt to solve:

Simplifying
5 + -6x = 0

Solving
5 + -6x = 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 + -6x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -6x = 0 + -5
-6x = 0 + -5

Combine like terms: 0 + -5 = -5
-6x = -5

Divide each side by '-6'.
x = 0.8333333333

Simplifying
x = 0.8333333333
Solution
x = {0.5, 0.8333333333}

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