5u(u+3)(u-7)=0

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Solution for 5u(u+3)(u-7)=0 equation: 


Simplifying
5u(u + 3)(u + -7) = 0

Reorder the terms:
5u(3 + u)(u + -7) = 0

Reorder the terms:
5u(3 + u)(-7 + u) = 0

Multiply (3 + u) * (-7 + u)
5u(3(-7 + u) + u(-7 + u)) = 0
5u((-7 * 3 + u * 3) + u(-7 + u)) = 0
5u((-21 + 3u) + u(-7 + u)) = 0
5u(-21 + 3u + (-7 * u + u * u)) = 0
5u(-21 + 3u + (-7u + u2)) = 0

Combine like terms: 3u + -7u = -4u
5u(-21 + -4u + u2) = 0
(-21 * 5u + -4u * 5u + u2 * 5u) = 0
(-105u + -20u2 + 5u3) = 0

Solving
-105u + -20u2 + 5u3 = 0

Solving for variable 'u'.

Factor out the Greatest Common Factor (GCF), '5u'.
5u(-21 + -4u + u2) = 0

Factor a trinomial.
5u((-3 + -1u)(7 + -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 '(-3 + -1u)' equal to zero and attempt to solve:

Simplifying
-3 + -1u = 0

Solving
-3 + -1u = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1u = 0 + 3

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

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

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

Simplifying
u = -3

Subproblem 3
Set the factor '(7 + -1u)' equal to zero and attempt to solve:

Simplifying
7 + -1u = 0

Solving
7 + -1u = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1u = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1u = 0 + -7
-1u = 0 + -7

Combine like terms: 0 + -7 = -7
-1u = -7

Divide each side by '-1'.
u = 7

Simplifying
u = 7
Solution
u = {0, -3, 7}

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