5w^2+41w+42=0

Solution for 5w^2+41w+42=0 equation:

Simplifying
5w2 + 41w + 42 = 0

Reorder the terms:
42 + 41w + 5w2 = 0

Solving
42 + 41w + 5w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(7 + w)(6 + 5w) = 0

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

Simplifying
7 + w = 0

Solving
7 + w = 0

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

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

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

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

Simplifying
w = -7
Subproblem 2
Set the factor '(6 + 5w)' equal to zero and attempt to solve:

Simplifying
6 + 5w = 0

Solving
6 + 5w = 0

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

Add '-6' to each side of the equation.
6 + -6 + 5w = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 5w = 0 + -6
5w = 0 + -6

Combine like terms: 0 + -6 = -6
5w = -6

Divide each side by '5'.
w = -1.2

Simplifying
w = -1.2
Solution
w = {-7, -1.2}