3u(u-4)(u+6)=0

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Solution for 3u(u-4)(u+6)=0 equation:


Simplifying
3u(u + -4)(u + 6) = 0

Reorder the terms:
3u(-4 + u)(u + 6) = 0

Reorder the terms:
3u(-4 + u)(6 + u) = 0

Multiply (-4 + u) * (6 + u)
3u(-4(6 + u) + u(6 + u)) = 0
3u((6 * -4 + u * -4) + u(6 + u)) = 0
3u((-24 + -4u) + u(6 + u)) = 0
3u(-24 + -4u + (6 * u + u * u)) = 0
3u(-24 + -4u + (6u + u2)) = 0

Combine like terms: -4u + 6u = 2u
3u(-24 + 2u + u2) = 0
(-24 * 3u + 2u * 3u + u2 * 3u) = 0
(-72u + 6u2 + 3u3) = 0

Solving
-72u + 6u2 + 3u3 = 0

Solving for variable 'u'.

Factor out the Greatest Common Factor (GCF), '3u'.
3u(-24 + 2u + u2) = 0

Factor a trinomial.
3u((-6 + -1u)(4 + -1u)) = 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 '(-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

Subproblem 3

Set the factor '(4 + -1u)' equal to zero and attempt to solve: Simplifying 4 + -1u = 0 Solving 4 + -1u = 0 Move all terms containing u to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1u = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1u = 0 + -4 -1u = 0 + -4 Combine like terms: 0 + -4 = -4 -1u = -4 Divide each side by '-1'. u = 4 Simplifying u = 4

Solution

u = {0, -6, 4}

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