5(4x-1)(6x-5)=0

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Solution for 5(4x-1)(6x-5)=0 equation: 


Simplifying
5(4x + -1)(6x + -5) = 0

Reorder the terms:
5(-1 + 4x)(6x + -5) = 0

Reorder the terms:
5(-1 + 4x)(-5 + 6x) = 0

Multiply (-1 + 4x) * (-5 + 6x)
5(-1(-5 + 6x) + 4x * (-5 + 6x)) = 0
5((-5 * -1 + 6x * -1) + 4x * (-5 + 6x)) = 0
5((5 + -6x) + 4x * (-5 + 6x)) = 0
5(5 + -6x + (-5 * 4x + 6x * 4x)) = 0
5(5 + -6x + (-20x + 24x2)) = 0

Combine like terms: -6x + -20x = -26x
5(5 + -26x + 24x2) = 0
(5 * 5 + -26x * 5 + 24x2 * 5) = 0
(25 + -130x + 120x2) = 0

Solving
25 + -130x + 120x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(5 + -26x + 24x2) = 0

Factor a trinomial.
5((1 + -4x)(5 + -6x)) = 0

Ignore the factor 5.

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

Simplifying
1 + -4x = 0

Solving
1 + -4x = 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 + -4x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -4x = 0 + -1
-4x = 0 + -1

Combine like terms: 0 + -1 = -1
-4x = -1

Divide each side by '-4'.
x = 0.25

Simplifying
x = 0.25

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 = {0.25, 0.8333333333}

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