(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 + x + x2) = 0

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

Ignore the factor 3.

Subproblem 1
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

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 = {-4, 3}

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