3(x+10)+6=3x(x+12)

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Solution for 3(x+10)+6=3x(x+12) equation: 


Simplifying
3(x + 10) + 6 = 3x(x + 12)

Reorder the terms:
3(10 + x) + 6 = 3x(x + 12)
(10 * 3 + x * 3) + 6 = 3x(x + 12)
(30 + 3x) + 6 = 3x(x + 12)

Reorder the terms:
30 + 6 + 3x = 3x(x + 12)

Combine like terms: 30 + 6 = 36
36 + 3x = 3x(x + 12)

Reorder the terms:
36 + 3x = 3x(12 + x)
36 + 3x = (12 * 3x + x * 3x)
36 + 3x = (36x + 3x2)

Solving
36 + 3x = 36x + 3x2

Solving for variable 'x'.

Combine like terms: 3x + -36x = -33x
36 + -33x + -3x2 = 36x + 3x2 + -36x + -3x2

Reorder the terms:
36 + -33x + -3x2 = 36x + -36x + 3x2 + -3x2

Combine like terms: 36x + -36x = 0
36 + -33x + -3x2 = 0 + 3x2 + -3x2
36 + -33x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
36 + -33x + -3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(12 + -11x + -1x2) = 0

Factor a trinomial.
3((1 + -1x)(12 + x)) = 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 '(12 + x)' equal to zero and attempt to solve:

Simplifying
12 + x = 0

Solving
12 + x = 0

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

Add '-12' to each side of the equation.
12 + -12 + x = 0 + -12

Combine like terms: 12 + -12 = 0
0 + x = 0 + -12
x = 0 + -12

Combine like terms: 0 + -12 = -12
x = -12

Simplifying
x = -12
Solution
x = {1, -12}

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