w^2-12w+36=2w^2-17w+30

Solution for w^2-12w+36=2w^2-17w+30 equation:

Simplifying
w2 + -12w + 36 = 2w2 + -17w + 30

Reorder the terms:
36 + -12w + w2 = 2w2 + -17w + 30

Reorder the terms:
36 + -12w + w2 = 30 + -17w + 2w2

Solving
36 + -12w + w2 = 30 + -17w + 2w2

Solving for variable 'w'.

Reorder the terms:
36 + -30 + -12w + 17w + w2 + -2w2 = 30 + -17w + 2w2 + -30 + 17w + -2w2

Combine like terms: 36 + -30 = 6
6 + -12w + 17w + w2 + -2w2 = 30 + -17w + 2w2 + -30 + 17w + -2w2

Combine like terms: -12w + 17w = 5w
6 + 5w + w2 + -2w2 = 30 + -17w + 2w2 + -30 + 17w + -2w2

Combine like terms: w2 + -2w2 = -1w2
6 + 5w + -1w2 = 30 + -17w + 2w2 + -30 + 17w + -2w2

Reorder the terms:
6 + 5w + -1w2 = 30 + -30 + -17w + 17w + 2w2 + -2w2

Combine like terms: 30 + -30 = 0
6 + 5w + -1w2 = 0 + -17w + 17w + 2w2 + -2w2
6 + 5w + -1w2 = -17w + 17w + 2w2 + -2w2

Combine like terms: -17w + 17w = 0
6 + 5w + -1w2 = 0 + 2w2 + -2w2
6 + 5w + -1w2 = 2w2 + -2w2

Combine like terms: 2w2 + -2w2 = 0
6 + 5w + -1w2 = 0

Factor a trinomial.
(6 + -1w)(1 + w) = 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 '(1 + w)' equal to zero and attempt to solve:

Simplifying
1 + w = 0

Solving
1 + w = 0

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

Add '-1' to each side of the equation.
1 + -1 + w = 0 + -1

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

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

Simplifying
w = -1
Solution
w = {6, -1}