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

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


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

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

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

Multiply (-6 + 9x) * (3 + 3x)
(-6(3 + 3x) + 9x * (3 + 3x)) = 0
((3 * -6 + 3x * -6) + 9x * (3 + 3x)) = 0
((-18 + -18x) + 9x * (3 + 3x)) = 0
(-18 + -18x + (3 * 9x + 3x * 9x)) = 0
(-18 + -18x + (27x + 27x2)) = 0

Combine like terms: -18x + 27x = 9x
(-18 + 9x + 27x2) = 0

Solving
-18 + 9x + 27x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '9'.
9(-2 + x + 3x2) = 0

Factor a trinomial.
9((-1 + -1x)(2 + -3x)) = 0

Ignore the factor 9.

Subproblem 1

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

Subproblem 2

Set the factor '(2 + -3x)' equal to zero and attempt to solve: Simplifying 2 + -3x = 0 Solving 2 + -3x = 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 + -3x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3x = 0 + -2 -3x = 0 + -2 Combine like terms: 0 + -2 = -2 -3x = -2 Divide each side by '-3'. x = 0.6666666667 Simplifying x = 0.6666666667

Solution

x = {-1, 0.6666666667}

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