(3x+8)(6x+9)=0

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Solution for (3x+8)(6x+9)=0 equation: 


Simplifying
(3x + 8)(6x + 9) = 0

Reorder the terms:
(8 + 3x)(6x + 9) = 0

Reorder the terms:
(8 + 3x)(9 + 6x) = 0

Multiply (8 + 3x) * (9 + 6x)
(8(9 + 6x) + 3x * (9 + 6x)) = 0
((9 * 8 + 6x * 8) + 3x * (9 + 6x)) = 0
((72 + 48x) + 3x * (9 + 6x)) = 0
(72 + 48x + (9 * 3x + 6x * 3x)) = 0
(72 + 48x + (27x + 18x2)) = 0

Combine like terms: 48x + 27x = 75x
(72 + 75x + 18x2) = 0

Solving
72 + 75x + 18x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(24 + 25x + 6x2) = 0

Factor a trinomial.
3((8 + 3x)(3 + 2x)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(8 + 3x)' equal to zero and attempt to solve:

Simplifying
8 + 3x = 0

Solving
8 + 3x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-8' to each side of the equation.
8 + -8 + 3x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + 3x = 0 + -8
3x = 0 + -8

Combine like terms: 0 + -8 = -8
3x = -8

Divide each side by '3'.
x = -2.666666667

Simplifying
x = -2.666666667

Subproblem 2
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
Solution
x = {-2.666666667, -1.5}

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