0=5w^2-23w-42

Solution for 0=5w^2-23w-42 equation:

Simplifying
0 = 5w2 + -23w + -42

Reorder the terms:
0 = -42 + -23w + 5w2

Solving
0 = -42 + -23w + 5w2

Solving for variable 'w'.

Combine like terms: 0 + 42 = 42
42 + 23w + -5w2 = -42 + -23w + 5w2 + 42 + 23w + -5w2

Reorder the terms:
42 + 23w + -5w2 = -42 + 42 + -23w + 23w + 5w2 + -5w2

Combine like terms: -42 + 42 = 0
42 + 23w + -5w2 = 0 + -23w + 23w + 5w2 + -5w2
42 + 23w + -5w2 = -23w + 23w + 5w2 + -5w2

Combine like terms: -23w + 23w = 0
42 + 23w + -5w2 = 0 + 5w2 + -5w2
42 + 23w + -5w2 = 5w2 + -5w2

Combine like terms: 5w2 + -5w2 = 0
42 + 23w + -5w2 = 0

Factor a trinomial.
(6 + -1w)(7 + 5w) = 0

Subproblem 1
Set the factor '(6 + -1w)' equal to zero and attempt to solve:

Simplifying
6 + -1w = 0

Solving
6 + -1w = 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 + -1w = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1w = 0 + -6
-1w = 0 + -6

Combine like terms: 0 + -6 = -6
-1w = -6

Divide each side by '-1'.
w = 6

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

Simplifying
7 + 5w = 0

Solving
7 + 5w = 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 + 5w = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 5w = 0 + -7
5w = 0 + -7

Combine like terms: 0 + -7 = -7
5w = -7

Divide each side by '5'.
w = -1.4

Simplifying
w = -1.4
Solution
w = {6, -1.4}