6=(5w+7)w

Solution for 6=(5w+7)w equation:

Simplifying
6 = (5w + 7) * w

Reorder the terms:
6 = (7 + 5w) * w

Reorder the terms for easier multiplication:
6 = w(7 + 5w)
6 = (7 * w + 5w * w)
6 = (7w + 5w2)

Solving
6 = 7w + 5w2

Solving for variable 'w'.

Reorder the terms:
6 + -7w + -5w2 = 7w + -7w + 5w2 + -5w2

Combine like terms: 7w + -7w = 0
6 + -7w + -5w2 = 0 + 5w2 + -5w2
6 + -7w + -5w2 = 5w2 + -5w2

Combine like terms: 5w2 + -5w2 = 0
6 + -7w + -5w2 = 0

Factor a trinomial.
(3 + -5w)(2 + w) = 0

Subproblem 1
Set the factor '(3 + -5w)' equal to zero and attempt to solve:

Simplifying
3 + -5w = 0

Solving
3 + -5w = 0

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

Add '-3' to each side of the equation.
3 + -3 + -5w = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -5w = 0 + -3
-5w = 0 + -3

Combine like terms: 0 + -3 = -3
-5w = -3

Divide each side by '-5'.
w = 0.6

Simplifying
w = 0.6
Subproblem 2
Set the factor '(2 + w)' equal to zero and attempt to solve:

Simplifying
2 + w = 0

Solving
2 + w = 0

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

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

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

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

Simplifying
w = -2
Solution
w = {0.6, -2}