(2x+4)(3x-9)=0

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Solution for (2x+4)(3x-9)=0 equation:


Simplifying
(2x + 4)(3x + -9) = 0

Reorder the terms:
(4 + 2x)(3x + -9) = 0

Reorder the terms:
(4 + 2x)(-9 + 3x) = 0

Multiply (4 + 2x) * (-9 + 3x)
(4(-9 + 3x) + 2x * (-9 + 3x)) = 0
((-9 * 4 + 3x * 4) + 2x * (-9 + 3x)) = 0
((-36 + 12x) + 2x * (-9 + 3x)) = 0
(-36 + 12x + (-9 * 2x + 3x * 2x)) = 0
(-36 + 12x + (-18x + 6x2)) = 0

Combine like terms: 12x + -18x = -6x
(-36 + -6x + 6x2) = 0

Solving
-36 + -6x + 6x2 = 0

Solving for variable 'x'.

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

Factor a trinomial.
6((-2 + -1x)(3 + -1x)) = 0

Ignore the factor 6.

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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