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

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

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

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

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

Multiply (-6 + x) * (-6 + 4x)
(-6(-6 + 4x) + x(-6 + 4x)) = 0
((-6 * -6 + 4x * -6) + x(-6 + 4x)) = 0
((36 + -24x) + x(-6 + 4x)) = 0
(36 + -24x + (-6 * x + 4x * x)) = 0
(36 + -24x + (-6x + 4x2)) = 0

Combine like terms: -24x + -6x = -30x
(36 + -30x + 4x2) = 0

Solving
36 + -30x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(18 + -15x + 2x2) = 0

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

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

Simplifying
3 + -2x = 0

Solving
3 + -2x = 0

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

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

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

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

Divide each side by '-2'.
x = 1.5

Simplifying
x = 1.5
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 = {1.5, 6}