3x(2x+6)(5x-15)=0

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Solution for 3x(2x+6)(5x-15)=0 equation: 


Simplifying
3x(2x + 6)(5x + -15) = 0

Reorder the terms:
3x(6 + 2x)(5x + -15) = 0

Reorder the terms:
3x(6 + 2x)(-15 + 5x) = 0

Multiply (6 + 2x) * (-15 + 5x)
3x(6(-15 + 5x) + 2x * (-15 + 5x)) = 0
3x((-15 * 6 + 5x * 6) + 2x * (-15 + 5x)) = 0
3x((-90 + 30x) + 2x * (-15 + 5x)) = 0
3x(-90 + 30x + (-15 * 2x + 5x * 2x)) = 0
3x(-90 + 30x + (-30x + 10x2)) = 0

Combine like terms: 30x + -30x = 0
3x(-90 + 0 + 10x2) = 0
3x(-90 + 10x2) = 0
(-90 * 3x + 10x2 * 3x) = 0
(-270x + 30x3) = 0

Solving
-270x + 30x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '30x'.
30x(-9 + x2) = 0

Factor a difference between two squares.
30x((3 + x)(-3 + x)) = 0

Ignore the factor 30.

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 '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 0

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

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

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

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

Simplifying
x = -3

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

Simplifying
-3 + x = 0

Solving
-3 + x = 0

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

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

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

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

Simplifying
x = 3
Solution
x = {0, -3, 3}

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