3x(x+2)(10x-5)=0

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Solution for 3x(x+2)(10x-5)=0 equation: 


Simplifying
3x(x + 2)(10x + -5) = 0

Reorder the terms:
3x(2 + x)(10x + -5) = 0

Reorder the terms:
3x(2 + x)(-5 + 10x) = 0

Multiply (2 + x) * (-5 + 10x)
3x(2(-5 + 10x) + x(-5 + 10x)) = 0
3x((-5 * 2 + 10x * 2) + x(-5 + 10x)) = 0
3x((-10 + 20x) + x(-5 + 10x)) = 0
3x(-10 + 20x + (-5 * x + 10x * x)) = 0
3x(-10 + 20x + (-5x + 10x2)) = 0

Combine like terms: 20x + -5x = 15x
3x(-10 + 15x + 10x2) = 0
(-10 * 3x + 15x * 3x + 10x2 * 3x) = 0
(-30x + 45x2 + 30x3) = 0

Solving
-30x + 45x2 + 30x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '15x'.
15x(-2 + 3x + 2x2) = 0

Factor a trinomial.
15x((-2 + -1x)(1 + -2x)) = 0

Ignore the factor 15.

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 + -1x)' equal to zero and attempt to solve:

Simplifying
-2 + -1x = 0

Solving
-2 + -1x = 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 + -1x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1x = 0 + 2
-1x = 0 + 2

Combine like terms: 0 + 2 = 2
-1x = 2

Divide each side by '-1'.
x = -2

Simplifying
x = -2

Subproblem 3
Set the factor '(1 + -2x)' equal to zero and attempt to solve:

Simplifying
1 + -2x = 0

Solving
1 + -2x = 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 + -2x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2x = 0 + -1
-2x = 0 + -1

Combine like terms: 0 + -1 = -1
-2x = -1

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5
Solution
x = {0, -2, 0.5}

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