3x(x-4)=3x-12

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Solution for 3x(x-4)=3x-12 equation:


Simplifying
3x(x + -4) = 3x + -12

Reorder the terms:
3x(-4 + x) = 3x + -12
(-4 * 3x + x * 3x) = 3x + -12
(-12x + 3x2) = 3x + -12

Reorder the terms:
-12x + 3x2 = -12 + 3x

Solving
-12x + 3x2 = -12 + 3x

Solving for variable 'x'.

Reorder the terms:
12 + -12x + -3x + 3x2 = -12 + 3x + 12 + -3x

Combine like terms: -12x + -3x = -15x
12 + -15x + 3x2 = -12 + 3x + 12 + -3x

Reorder the terms:
12 + -15x + 3x2 = -12 + 12 + 3x + -3x

Combine like terms: -12 + 12 = 0
12 + -15x + 3x2 = 0 + 3x + -3x
12 + -15x + 3x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
12 + -15x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(4 + -5x + x2) = 0

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

Ignore the factor 3.

Subproblem 1
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

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 = {1, 4}

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