(3x-21)(x+12)=0

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Solution for (3x-21)(x+12)=0 equation: 


Simplifying
(3x + -21)(x + 12) = 0

Reorder the terms:
(-21 + 3x)(x + 12) = 0

Reorder the terms:
(-21 + 3x)(12 + x) = 0

Multiply (-21 + 3x) * (12 + x)
(-21(12 + x) + 3x * (12 + x)) = 0
((12 * -21 + x * -21) + 3x * (12 + x)) = 0
((-252 + -21x) + 3x * (12 + x)) = 0
(-252 + -21x + (12 * 3x + x * 3x)) = 0
(-252 + -21x + (36x + 3x2)) = 0

Combine like terms: -21x + 36x = 15x
(-252 + 15x + 3x2) = 0

Solving
-252 + 15x + 3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-84 + 5x + x2) = 0

Factor a trinomial.
3((-12 + -1x)(7 + -1x)) = 0

Ignore the factor 3.

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 '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {-12, 7}

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