(3x-9)*(x+2)=0

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Solution for (3x-9)*(x+2)=0 equation:


Simplifying
(3x + -9)(x + 2) = 0

Reorder the terms:
(-9 + 3x)(x + 2) = 0

Reorder the terms:
(-9 + 3x)(2 + x) = 0

Multiply (-9 + 3x) * (2 + x)
(-9(2 + x) + 3x * (2 + x)) = 0
((2 * -9 + x * -9) + 3x * (2 + x)) = 0
((-18 + -9x) + 3x * (2 + x)) = 0
(-18 + -9x + (2 * 3x + x * 3x)) = 0
(-18 + -9x + (6x + 3x2)) = 0

Combine like terms: -9x + 6x = -3x
(-18 + -3x + 3x2) = 0

Solving
-18 + -3x + 3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-6 + -1x + x2) = 0

Factor a trinomial.
3((-2 + -1x)(3 + -1x)) = 0

Ignore the factor 3.

Subproblem 1

Set the factor '(-2 + -1x)' equal to zero and attempt to solve: Simplifying -2 + -1x = 0 Solving -2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -1x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1x = 0 + 2 -1x = 0 + 2 Combine like terms: 0 + 2 = 2 -1x = 2 Divide each side by '-1'. x = -2 Simplifying x = -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 = {-2, 3}

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