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

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


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

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

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

Multiply (5 + 2x) * (-2 + 3x)
3(5(-2 + 3x) + 2x * (-2 + 3x)) = 0
3((-2 * 5 + 3x * 5) + 2x * (-2 + 3x)) = 0
3((-10 + 15x) + 2x * (-2 + 3x)) = 0
3(-10 + 15x + (-2 * 2x + 3x * 2x)) = 0
3(-10 + 15x + (-4x + 6x2)) = 0

Combine like terms: 15x + -4x = 11x
3(-10 + 11x + 6x2) = 0
(-10 * 3 + 11x * 3 + 6x2 * 3) = 0
(-30 + 33x + 18x2) = 0

Solving
-30 + 33x + 18x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-10 + 11x + 6x2) = 0

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

Ignore the factor 3.

Subproblem 1
Set the factor '(-5 + -2x)' equal to zero and attempt to solve:

Simplifying
-5 + -2x = 0

Solving
-5 + -2x = 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 + -2x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -2x = 0 + 5
-2x = 0 + 5

Combine like terms: 0 + 5 = 5
-2x = 5

Divide each side by '-2'.
x = -2.5

Simplifying
x = -2.5

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 = {-2.5, 0.6666666667}

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