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

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


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

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

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

Combine like terms: 9x + 36x = 45x
(-36 + 45x + -9x2) = 0

Solving
-36 + 45x + -9x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '9'.
9(-4 + 5x + -1x2) = 0

Factor a trinomial.
9((-4 + x)(1 + -1x)) = 0

Ignore the factor 9.

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

Simplifying
-4 + x = 0

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

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

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

Simplifying
x = 4

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

Simplifying
1 + -1x = 0

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

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

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

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

Simplifying
x = 1
Solution
x = {4, 1}

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