(x)(2-5x)(1+3x)=0

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Solution for (x)(2-5x)(1+3x)=0 equation: 


Simplifying
(x)(2 + -5x)(1 + 3x) = 0

Multiply (2 + -5x) * (1 + 3x)
x(2(1 + 3x) + -5x * (1 + 3x)) = 0
x((1 * 2 + 3x * 2) + -5x * (1 + 3x)) = 0
x((2 + 6x) + -5x * (1 + 3x)) = 0
x(2 + 6x + (1 * -5x + 3x * -5x)) = 0
x(2 + 6x + (-5x + -15x2)) = 0

Combine like terms: 6x + -5x = 1x
x(2 + 1x + -15x2) = 0
(2 * x + 1x * x + -15x2 * x) = 0
(2x + 1x2 + -15x3) = 0

Solving
2x + 1x2 + -15x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(2 + x + -15x2) = 0

Factor a trinomial.
x((2 + -5x)(1 + 3x)) = 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 + -5x)' equal to zero and attempt to solve:

Simplifying
2 + -5x = 0

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

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

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

Divide each side by '-5'.
x = 0.4

Simplifying
x = 0.4

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

Simplifying
1 + 3x = 0

Solving
1 + 3x = 0

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

Add '-1' to each side of the equation.
1 + -1 + 3x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 3x = 0 + -1
3x = 0 + -1

Combine like terms: 0 + -1 = -1
3x = -1

Divide each side by '3'.
x = -0.3333333333

Simplifying
x = -0.3333333333
Solution
x = {0, 0.4, -0.3333333333}

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