4u(u+7)(u-6)=0

Solution for 4u(u+7)(u-6)=0 equation:

Simplifying
4u(u + 7)(u + -6) = 0

Reorder the terms:
4u(7 + u)(u + -6) = 0

Reorder the terms:
4u(7 + u)(-6 + u) = 0

Multiply (7 + u) * (-6 + u)
4u(7(-6 + u) + u(-6 + u)) = 0
4u((-6 * 7 + u * 7) + u(-6 + u)) = 0
4u((-42 + 7u) + u(-6 + u)) = 0
4u(-42 + 7u + (-6 * u + u * u)) = 0
4u(-42 + 7u + (-6u + u2)) = 0

Combine like terms: 7u + -6u = 1u
4u(-42 + 1u + u2) = 0
(-42 * 4u + 1u * 4u + u2 * 4u) = 0
(-168u + 4u2 + 4u3) = 0

Solving
-168u + 4u2 + 4u3 = 0

Solving for variable 'u'.

Factor out the Greatest Common Factor (GCF), '4u'.
4u(-42 + u + u2) = 0

Factor a trinomial.
4u((-7 + -1u)(6 + -1u)) = 0

Ignore the factor 4.
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 '(-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
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, -7, 6}