5u(u+9)(u-6)=0

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Solution for 5u(u+9)(u-6)=0 equation: 


Simplifying
5u(u + 9)(u + -6) = 0

Reorder the terms:
5u(9 + u)(u + -6) = 0

Reorder the terms:
5u(9 + u)(-6 + u) = 0

Multiply (9 + u) * (-6 + u)
5u(9(-6 + u) + u(-6 + u)) = 0
5u((-6 * 9 + u * 9) + u(-6 + u)) = 0
5u((-54 + 9u) + u(-6 + u)) = 0
5u(-54 + 9u + (-6 * u + u * u)) = 0
5u(-54 + 9u + (-6u + u2)) = 0

Combine like terms: 9u + -6u = 3u
5u(-54 + 3u + u2) = 0
(-54 * 5u + 3u * 5u + u2 * 5u) = 0
(-270u + 15u2 + 5u3) = 0

Solving
-270u + 15u2 + 5u3 = 0

Solving for variable 'u'.

Factor out the Greatest Common Factor (GCF), '5u'.
5u(-54 + 3u + u2) = 0

Factor a trinomial.
5u((-9 + -1u)(6 + -1u)) = 0

Ignore the factor 5.

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 '(-9 + -1u)' equal to zero and attempt to solve:

Simplifying
-9 + -1u = 0

Solving
-9 + -1u = 0

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

Add '9' to each side of the equation.
-9 + 9 + -1u = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1u = 0 + 9
-1u = 0 + 9

Combine like terms: 0 + 9 = 9
-1u = 9

Divide each side by '-1'.
u = -9

Simplifying
u = -9

Subproblem 3
Set the factor '(6 + -1u)' equal to zero and attempt to solve:

Simplifying
6 + -1u = 0

Solving
6 + -1u = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1u = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1u = 0 + -6
-1u = 0 + -6

Combine like terms: 0 + -6 = -6
-1u = -6

Divide each side by '-1'.
u = 6

Simplifying
u = 6
Solution
u = {0, -9, 6}

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