(3x-9)(5x+6)=0

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Solution for (3x-9)(5x+6)=0 equation:


Simplifying
(3x + -9)(5x + 6) = 0

Reorder the terms:
(-9 + 3x)(5x + 6) = 0

Reorder the terms:
(-9 + 3x)(6 + 5x) = 0

Multiply (-9 + 3x) * (6 + 5x)
(-9(6 + 5x) + 3x * (6 + 5x)) = 0
((6 * -9 + 5x * -9) + 3x * (6 + 5x)) = 0
((-54 + -45x) + 3x * (6 + 5x)) = 0
(-54 + -45x + (6 * 3x + 5x * 3x)) = 0
(-54 + -45x + (18x + 15x2)) = 0

Combine like terms: -45x + 18x = -27x
(-54 + -27x + 15x2) = 0

Solving
-54 + -27x + 15x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-18 + -9x + 5x2) = 0

Factor a trinomial.
3((-6 + -5x)(3 + -1x)) = 0

Ignore the factor 3.

Subproblem 1

Set the factor '(-6 + -5x)' equal to zero and attempt to solve: Simplifying -6 + -5x = 0 Solving -6 + -5x = 0 Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + -5x = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -5x = 0 + 6 -5x = 0 + 6 Combine like terms: 0 + 6 = 6 -5x = 6 Divide each side by '-5'. x = -1.2 Simplifying x = -1.2

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 = {-1.2, 3}

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