x^2(-3-x)(5-x)=0

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


Simplifying
x2(-3 + -1x)(5 + -1x) = 0

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

Combine like terms: 3x + -5x = -2x
x2(-15 + -2x + 1x2) = 0
(-15 * x2 + -2x * x2 + 1x2 * x2) = 0
(-15x2 + -2x3 + 1x4) = 0

Solving
-15x2 + -2x3 + 1x4 = 0

Solving for variable 'x'.

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

Factor a trinomial.
x2((-3 + -1x)(5 + -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 '(-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

Subproblem 3
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 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 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {0, -3, 5}

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