(x-2)(3x-12)=0

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Solution for (x-2)(3x-12)=0 equation: 


Simplifying
(x + -2)(3x + -12) = 0

Reorder the terms:
(-2 + x)(3x + -12) = 0

Reorder the terms:
(-2 + x)(-12 + 3x) = 0

Multiply (-2 + x) * (-12 + 3x)
(-2(-12 + 3x) + x(-12 + 3x)) = 0
((-12 * -2 + 3x * -2) + x(-12 + 3x)) = 0
((24 + -6x) + x(-12 + 3x)) = 0
(24 + -6x + (-12 * x + 3x * x)) = 0
(24 + -6x + (-12x + 3x2)) = 0

Combine like terms: -6x + -12x = -18x
(24 + -18x + 3x2) = 0

Solving
24 + -18x + 3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(8 + -6x + x2) = 0

Factor a trinomial.
3((2 + -1x)(4 + -1x)) = 0

Ignore the factor 3.

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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

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

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

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

Divide each side by '-1'.
x = 2

Simplifying
x = 2

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 = {2, 4}

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