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

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


Simplifying
(3x2 + -1x)(x2 + 5x) = 0

Reorder the terms:
(-1x + 3x2)(x2 + 5x) = 0

Reorder the terms:
(-1x + 3x2)(5x + x2) = 0

Multiply (-1x + 3x2) * (5x + x2)
(-1x * (5x + x2) + 3x2 * (5x + x2)) = 0
((5x * -1x + x2 * -1x) + 3x2 * (5x + x2)) = 0
((-5x2 + -1x3) + 3x2 * (5x + x2)) = 0
(-5x2 + -1x3 + (5x * 3x2 + x2 * 3x2)) = 0
(-5x2 + -1x3 + (15x3 + 3x4)) = 0

Combine like terms: -1x3 + 15x3 = 14x3
(-5x2 + 14x3 + 3x4) = 0

Solving
-5x2 + 14x3 + 3x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(-5 + 14x + 3x2) = 0

Factor a trinomial.
x2((-5 + -1x)(1 + -3x)) = 0


Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve:

Simplifying
x2 = 0

Solving
x2 = 0

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

Simplifying
x2 = 0

Take the square root of each side:
x = {0}

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

Simplifying
-5 + -1x = 0

Solving
-5 + -1x = 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 + -1x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1x = 0 + 5
-1x = 0 + 5

Combine like terms: 0 + 5 = 5
-1x = 5

Divide each side by '-1'.
x = -5

Simplifying
x = -5

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, -5, 0.3333333333}

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