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

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


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

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

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

Multiply (-9 + 4x) * (9 + 3x)
(-9(9 + 3x) + 4x * (9 + 3x)) = 0
((9 * -9 + 3x * -9) + 4x * (9 + 3x)) = 0
((-81 + -27x) + 4x * (9 + 3x)) = 0
(-81 + -27x + (9 * 4x + 3x * 4x)) = 0
(-81 + -27x + (36x + 12x2)) = 0

Combine like terms: -27x + 36x = 9x
(-81 + 9x + 12x2) = 0

Solving
-81 + 9x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-27 + 3x + 4x2) = 0

Factor a trinomial.
3((-3 + -1x)(9 + -4x)) = 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 '(9 + -4x)' equal to zero and attempt to solve:

Simplifying
9 + -4x = 0

Solving
9 + -4x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -4x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -4x = 0 + -9
-4x = 0 + -9

Combine like terms: 0 + -9 = -9
-4x = -9

Divide each side by '-4'.
x = 2.25

Simplifying
x = 2.25
Solution
x = {-3, 2.25}

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