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

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


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

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

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

Multiply (6 + 3x) * (6 + 9x)
(6(6 + 9x) + 3x * (6 + 9x)) = 0
((6 * 6 + 9x * 6) + 3x * (6 + 9x)) = 0
((36 + 54x) + 3x * (6 + 9x)) = 0
(36 + 54x + (6 * 3x + 9x * 3x)) = 0
(36 + 54x + (18x + 27x2)) = 0

Combine like terms: 54x + 18x = 72x
(36 + 72x + 27x2) = 0

Solving
36 + 72x + 27x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '9'.
9(4 + 8x + 3x2) = 0

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

Ignore the factor 9.

Subproblem 1

Set the factor '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 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 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Simplifying x = -2

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 = {-2, -0.6666666667}

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