-3u^2-15u+42=0

Solution for -3u^2-15u+42=0 equation:

Simplifying
-3u2 + -15u + 42 = 0

Reorder the terms:
42 + -15u + -3u2 = 0

Solving
42 + -15u + -3u2 = 0

Solving for variable 'u'.

Factor out the Greatest Common Factor (GCF), '3'.
3(14 + -5u + -1u2) = 0

Factor a trinomial.
3((2 + -1u)(7 + u)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(2 + -1u)' equal to zero and attempt to solve:

Simplifying
2 + -1u = 0

Solving
2 + -1u = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1u = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1u = 0 + -2
-1u = 0 + -2

Combine like terms: 0 + -2 = -2
-1u = -2

Divide each side by '-1'.
u = 2

Simplifying
u = 2
Subproblem 2
Set the factor '(7 + u)' equal to zero and attempt to solve:

Simplifying
7 + u = 0

Solving
7 + u = 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 + u = 0 + -7

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

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

Simplifying
u = -7
Solution
u = {2, -7}