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

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


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

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

Combine like terms: 4x + -15x = -11x
x(10 + -11x + -6x2) = 0
(10 * x + -11x * x + -6x2 * x) = 0
(10x + -11x2 + -6x3) = 0

Solving
10x + -11x2 + -6x3 = 0

Solving for variable 'x'.

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

Factor a trinomial.
x((2 + -3x)(5 + 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 '(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 '(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
Solution
x = {0, 0.6666666667, -2.5}

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