42=(5+2w)w

Solution for 42=(5+2w)w equation:

Simplifying
42 = (5 + 2w) * w

Reorder the terms for easier multiplication:
42 = w(5 + 2w)
42 = (5 * w + 2w * w)
42 = (5w + 2w2)

Solving
42 = 5w + 2w2

Solving for variable 'w'.

Reorder the terms:
42 + -5w + -2w2 = 5w + -5w + 2w2 + -2w2

Combine like terms: 5w + -5w = 0
42 + -5w + -2w2 = 0 + 2w2 + -2w2
42 + -5w + -2w2 = 2w2 + -2w2

Combine like terms: 2w2 + -2w2 = 0
42 + -5w + -2w2 = 0

Factor a trinomial.
(7 + -2w)(6 + w) = 0

Subproblem 1
Set the factor '(7 + -2w)' equal to zero and attempt to solve:

Simplifying
7 + -2w = 0

Solving
7 + -2w = 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 + -2w = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -2w = 0 + -7
-2w = 0 + -7

Combine like terms: 0 + -7 = -7
-2w = -7

Divide each side by '-2'.
w = 3.5

Simplifying
w = 3.5
Subproblem 2
Set the factor '(6 + w)' equal to zero and attempt to solve:

Simplifying
6 + w = 0

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

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

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

Simplifying
w = -6
Solution
w = {3.5, -6}