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

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


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

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

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

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

Combine like terms: 10x + -9x = 1x
x(-15 + 1x + 6x2) = 0
(-15 * x + 1x * x + 6x2 * x) = 0
(-15x + 1x2 + 6x3) = 0

Solving
-15x + 1x2 + 6x3 = 0

Solving for variable 'x'.

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

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


Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
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 3
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 = {0, -1.666666667, 1.5}

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