x^2(x+15)(x+3)=0

Solution for x^2(x+15)(x+3)=0 equation:

Simplifying
x2(x + 15)(x + 3) = 0

Reorder the terms:
x2(15 + x)(x + 3) = 0

Reorder the terms:
x2(15 + x)(3 + x) = 0

Multiply (15 + x) * (3 + x)
x2(15(3 + x) + x(3 + x)) = 0
x2((3 * 15 + x * 15) + x(3 + x)) = 0
x2((45 + 15x) + x(3 + x)) = 0
x2(45 + 15x + (3 * x + x * x)) = 0
x2(45 + 15x + (3x + x2)) = 0

Combine like terms: 15x + 3x = 18x
x2(45 + 18x + x2) = 0
(45 * x2 + 18x * x2 + x2 * x2) = 0
(45x2 + 18x3 + x4) = 0

Solving
45x2 + 18x3 + x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(45 + 18x + x2) = 0

Factor a trinomial.
x2((15 + x)(3 + x)) = 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 '(15 + x)' equal to zero and attempt to solve:

Simplifying
15 + x = 0

Solving
15 + x = 0

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

Add '-15' to each side of the equation.
15 + -15 + x = 0 + -15

Combine like terms: 15 + -15 = 0
0 + x = 0 + -15
x = 0 + -15

Combine like terms: 0 + -15 = -15
x = -15

Simplifying
x = -15
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, -15, -3}