-3u(u+5)(u-2)=0

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


Simplifying
-3u(u + 5)(u + -2) = 0

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

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

Multiply (5 + u) * (-2 + u)
-3u(5(-2 + u) + u(-2 + u)) = 0
-3u((-2 * 5 + u * 5) + u(-2 + u)) = 0
-3u((-10 + 5u) + u(-2 + u)) = 0
-3u(-10 + 5u + (-2 * u + u * u)) = 0
-3u(-10 + 5u + (-2u + u2)) = 0

Combine like terms: 5u + -2u = 3u
-3u(-10 + 3u + u2) = 0
(-10 * -3u + 3u * -3u + u2 * -3u) = 0
(30u + -9u2 + -3u3) = 0

Solving
30u + -9u2 + -3u3 = 0

Solving for variable 'u'.

Factor out the Greatest Common Factor (GCF), '3u'.
3u(10 + -3u + -1u2) = 0

Factor a trinomial.
3u((2 + -1u)(5 + u)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor 'u' equal to zero and attempt to solve:

Simplifying
u = 0

Solving
u = 0

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

Simplifying
u = 0

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

Simplifying
2 + -1u = 0

Solving
2 + -1u = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1u = 0 + -2

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

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

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

Simplifying
u = 2

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

Simplifying
5 + u = 0

Solving
5 + u = 0

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

Add '-5' to each side of the equation.
5 + -5 + u = 0 + -5

Combine like terms: 5 + -5 = 0
0 + u = 0 + -5
u = 0 + -5

Combine like terms: 0 + -5 = -5
u = -5

Simplifying
u = -5
Solution
u = {0, 2, -5}

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