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

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


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

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

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

Multiply (6 + 9x) * (9 + 6x)
(6(9 + 6x) + 9x * (9 + 6x)) = 0
((9 * 6 + 6x * 6) + 9x * (9 + 6x)) = 0
((54 + 36x) + 9x * (9 + 6x)) = 0
(54 + 36x + (9 * 9x + 6x * 9x)) = 0
(54 + 36x + (81x + 54x2)) = 0

Combine like terms: 36x + 81x = 117x
(54 + 117x + 54x2) = 0

Solving
54 + 117x + 54x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '9'.
9(6 + 13x + 6x2) = 0

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

Ignore the factor 9.

Subproblem 1

Set the factor '(3 + 2x)' equal to zero and attempt to solve: Simplifying 3 + 2x = 0 Solving 3 + 2x = 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 + 2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2x = 0 + -3 2x = 0 + -3 Combine like terms: 0 + -3 = -3 2x = -3 Divide each side by '2'. x = -1.5 Simplifying x = -1.5

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 = {-1.5, -0.6666666667}

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