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

Solution for 2(x-6)(4x-5)=0 equation:

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

Reorder the terms:
2(-6 + x)(4x + -5) = 0

Reorder the terms:
2(-6 + x)(-5 + 4x) = 0

Multiply (-6 + x) * (-5 + 4x)
2(-6(-5 + 4x) + x(-5 + 4x)) = 0
2((-5 * -6 + 4x * -6) + x(-5 + 4x)) = 0
2((30 + -24x) + x(-5 + 4x)) = 0
2(30 + -24x + (-5 * x + 4x * x)) = 0
2(30 + -24x + (-5x + 4x2)) = 0

Combine like terms: -24x + -5x = -29x
2(30 + -29x + 4x2) = 0
(30 * 2 + -29x * 2 + 4x2 * 2) = 0
(60 + -58x + 8x2) = 0

Solving
60 + -58x + 8x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(30 + -29x + 4x2) = 0

Factor a trinomial.
2((5 + -4x)(6 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
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
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 = {1.25, 6}