3x(x+12)-5(x+12)=0

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Solution for 3x(x+12)-5(x+12)=0 equation: 


Simplifying
3x(x + 12) + -5(x + 12) = 0

Reorder the terms:
3x(12 + x) + -5(x + 12) = 0
(12 * 3x + x * 3x) + -5(x + 12) = 0
(36x + 3x2) + -5(x + 12) = 0

Reorder the terms:
36x + 3x2 + -5(12 + x) = 0
36x + 3x2 + (12 * -5 + x * -5) = 0
36x + 3x2 + (-60 + -5x) = 0

Reorder the terms:
-60 + 36x + -5x + 3x2 = 0

Combine like terms: 36x + -5x = 31x
-60 + 31x + 3x2 = 0

Solving
-60 + 31x + 3x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-12 + -1x)(5 + -3x) = 0


Subproblem 1
Set the factor '(-12 + -1x)' equal to zero and attempt to solve:

Simplifying
-12 + -1x = 0

Solving
-12 + -1x = 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 + -1x = 0 + 12

Combine like terms: -12 + 12 = 0
0 + -1x = 0 + 12
-1x = 0 + 12

Combine like terms: 0 + 12 = 12
-1x = 12

Divide each side by '-1'.
x = -12

Simplifying
x = -12

Subproblem 2
Set the factor '(5 + -3x)' equal to zero and attempt to solve:

Simplifying
5 + -3x = 0

Solving
5 + -3x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -3x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -3x = 0 + -5
-3x = 0 + -5

Combine like terms: 0 + -5 = -5
-3x = -5

Divide each side by '-3'.
x = 1.666666667

Simplifying
x = 1.666666667
Solution
x = {-12, 1.666666667}

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