2(3x-9)(x-4)=0

Solution for 2(3x-9)(x-4)=0 equation:

Simplifying
2(3x + -9)(x + -4) = 0

Reorder the terms:
2(-9 + 3x)(x + -4) = 0

Reorder the terms:
2(-9 + 3x)(-4 + x) = 0

Multiply (-9 + 3x) * (-4 + x)
2(-9(-4 + x) + 3x * (-4 + x)) = 0
2((-4 * -9 + x * -9) + 3x * (-4 + x)) = 0
2((36 + -9x) + 3x * (-4 + x)) = 0
2(36 + -9x + (-4 * 3x + x * 3x)) = 0
2(36 + -9x + (-12x + 3x2)) = 0

Combine like terms: -9x + -12x = -21x
2(36 + -21x + 3x2) = 0
(36 * 2 + -21x * 2 + 3x2 * 2) = 0
(72 + -42x + 6x2) = 0

Solving
72 + -42x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6'.
6(12 + -7x + x2) = 0

Factor a trinomial.
6((3 + -1x)(4 + -1x)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 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 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

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

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

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {3, 4}