w+5w^2=-7w^2+(w+6)

Solution for w+5w^2=-7w^2+(w+6) equation:

Simplifying
w + 5w2 = -7w2 + (w + 6)

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

Remove parenthesis around (6 + w)
w + 5w2 = -7w2 + 6 + w

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

Add '-1w' to each side of the equation.
w + -1w + 5w2 = 6 + w + -1w + -7w2

Combine like terms: w + -1w = 0
0 + 5w2 = 6 + w + -1w + -7w2
5w2 = 6 + w + -1w + -7w2

Combine like terms: w + -1w = 0
5w2 = 6 + 0 + -7w2
5w2 = 6 + -7w2

Solving
5w2 = 6 + -7w2

Solving for variable 'w'.

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

Add '7w2' to each side of the equation.
5w2 + 7w2 = 6 + -7w2 + 7w2

Combine like terms: 5w2 + 7w2 = 12w2
12w2 = 6 + -7w2 + 7w2

Combine like terms: -7w2 + 7w2 = 0
12w2 = 6 + 0
12w2 = 6

Divide each side by '12'.
w2 = 0.5

Simplifying
w2 = 0.5

Take the square root of each side:
w = {-0.707106781, 0.707106781}