(4x-12)(9x+63)=0

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Solution for (4x-12)(9x+63)=0 equation: 


Simplifying
(4x + -12)(9x + 63) = 0

Reorder the terms:
(-12 + 4x)(9x + 63) = 0

Reorder the terms:
(-12 + 4x)(63 + 9x) = 0

Multiply (-12 + 4x) * (63 + 9x)
(-12(63 + 9x) + 4x * (63 + 9x)) = 0
((63 * -12 + 9x * -12) + 4x * (63 + 9x)) = 0
((-756 + -108x) + 4x * (63 + 9x)) = 0
(-756 + -108x + (63 * 4x + 9x * 4x)) = 0
(-756 + -108x + (252x + 36x2)) = 0

Combine like terms: -108x + 252x = 144x
(-756 + 144x + 36x2) = 0

Solving
-756 + 144x + 36x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '36'.
36(-21 + 4x + x2) = 0

Factor a trinomial.
36((-7 + -1x)(3 + -1x)) = 0

Ignore the factor 36.

Subproblem 1
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

Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-7, 3}

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