-6u^2+36u+42=0

Solution for -6u^2+36u+42=0 equation:

Simplifying
-6u2 + 36u + 42 = 0

Reorder the terms:
42 + 36u + -6u2 = 0

Solving
42 + 36u + -6u2 = 0

Solving for variable 'u'.

Factor out the Greatest Common Factor (GCF), '6'.
6(7 + 6u + -1u2) = 0

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

Ignore the factor 6.
Subproblem 1
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 2
Set the factor '(1 + u)' equal to zero and attempt to solve:

Simplifying
1 + u = 0

Solving
1 + u = 0

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

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

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

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

Simplifying
u = -1
Solution
u = {7, -1}