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

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

Simplifying
x2(2x + 1)(x + -3) = 0

Reorder the terms:
x2(1 + 2x)(x + -3) = 0

Reorder the terms:
x2(1 + 2x)(-3 + x) = 0

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

Combine like terms: 1x + -6x = -5x
x2(-3 + -5x + 2x2) = 0
(-3 * x2 + -5x * x2 + 2x2 * x2) = 0
(-3x2 + -5x3 + 2x4) = 0

Solving
-3x2 + -5x3 + 2x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(-3 + -5x + 2x2) = 0

Factor a trinomial.
x2((-1 + -2x)(3 + -1x)) = 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 '(-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
Subproblem 3
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 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 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {0, -0.5, 3}