3(3x+5)(2x+3)=0

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Solution for 3(3x+5)(2x+3)=0 equation: 


Simplifying
3(3x + 5)(2x + 3) = 0

Reorder the terms:
3(5 + 3x)(2x + 3) = 0

Reorder the terms:
3(5 + 3x)(3 + 2x) = 0

Multiply (5 + 3x) * (3 + 2x)
3(5(3 + 2x) + 3x * (3 + 2x)) = 0
3((3 * 5 + 2x * 5) + 3x * (3 + 2x)) = 0
3((15 + 10x) + 3x * (3 + 2x)) = 0
3(15 + 10x + (3 * 3x + 2x * 3x)) = 0
3(15 + 10x + (9x + 6x2)) = 0

Combine like terms: 10x + 9x = 19x
3(15 + 19x + 6x2) = 0
(15 * 3 + 19x * 3 + 6x2 * 3) = 0
(45 + 57x + 18x2) = 0

Solving
45 + 57x + 18x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(15 + 19x + 6x2) = 0

Factor a trinomial.
3((5 + 3x)(3 + 2x)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(5 + 3x)' equal to zero and attempt to solve:

Simplifying
5 + 3x = 0

Solving
5 + 3x = 0

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

Add '-5' to each side of the equation.
5 + -5 + 3x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 3x = 0 + -5
3x = 0 + -5

Combine like terms: 0 + -5 = -5
3x = -5

Divide each side by '3'.
x = -1.666666667

Simplifying
x = -1.666666667

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 = {-1.666666667, -1.5}

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