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

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


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

Reorder the terms:
2x(5 + 2x)(3x + -1) = 0

Reorder the terms:
2x(5 + 2x)(-1 + 3x) = 0

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

Combine like terms: 15x + -2x = 13x
2x(-5 + 13x + 6x2) = 0
(-5 * 2x + 13x * 2x + 6x2 * 2x) = 0
(-10x + 26x2 + 12x3) = 0

Solving
-10x + 26x2 + 12x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(-5 + 13x + 6x2) = 0

Factor a trinomial.
2x((-5 + -2x)(1 + -3x)) = 0

Ignore the factor 2.

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 + -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

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, -2.5, 0.3333333333}

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