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

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


Simplifying
(5x2 + -3x)(3x + 2) = 0

Reorder the terms:
(-3x + 5x2)(3x + 2) = 0

Reorder the terms:
(-3x + 5x2)(2 + 3x) = 0

Multiply (-3x + 5x2) * (2 + 3x)
(-3x * (2 + 3x) + 5x2 * (2 + 3x)) = 0
((2 * -3x + 3x * -3x) + 5x2 * (2 + 3x)) = 0
((-6x + -9x2) + 5x2 * (2 + 3x)) = 0
(-6x + -9x2 + (2 * 5x2 + 3x * 5x2)) = 0
(-6x + -9x2 + (10x2 + 15x3)) = 0

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

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

Solving for variable 'x'.

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

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

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

Simplifying
3 + -5x = 0

Solving
3 + -5x = 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 + -5x = 0 + -3

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

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

Divide each side by '-5'.
x = 0.6

Simplifying
x = 0.6
Solution
x = {0, -0.6666666667, 0.6}

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