(x-4)(3x+9)=0

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Solution for (x-4)(3x+9)=0 equation: 


Simplifying
(x + -4)(3x + 9) = 0

Reorder the terms:
(-4 + x)(3x + 9) = 0

Reorder the terms:
(-4 + x)(9 + 3x) = 0

Multiply (-4 + x) * (9 + 3x)
(-4(9 + 3x) + x(9 + 3x)) = 0
((9 * -4 + 3x * -4) + x(9 + 3x)) = 0
((-36 + -12x) + x(9 + 3x)) = 0
(-36 + -12x + (9 * x + 3x * x)) = 0
(-36 + -12x + (9x + 3x2)) = 0

Combine like terms: -12x + 9x = -3x
(-36 + -3x + 3x2) = 0

Solving
-36 + -3x + 3x2 = 0

Solving for variable 'x'.

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

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

Ignore the factor 3.

Subproblem 1
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

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 = {-3, 4}

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