w^2+6w+9=2w^2+8w-15

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Solution for w^2+6w+9=2w^2+8w-15 equation: 


Simplifying
w2 + 6w + 9 = 2w2 + 8w + -15

Reorder the terms:
9 + 6w + w2 = 2w2 + 8w + -15

Reorder the terms:
9 + 6w + w2 = -15 + 8w + 2w2

Solving
9 + 6w + w2 = -15 + 8w + 2w2

Solving for variable 'w'.

Reorder the terms:
9 + 15 + 6w + -8w + w2 + -2w2 = -15 + 8w + 2w2 + 15 + -8w + -2w2

Combine like terms: 9 + 15 = 24
24 + 6w + -8w + w2 + -2w2 = -15 + 8w + 2w2 + 15 + -8w + -2w2

Combine like terms: 6w + -8w = -2w
24 + -2w + w2 + -2w2 = -15 + 8w + 2w2 + 15 + -8w + -2w2

Combine like terms: w2 + -2w2 = -1w2
24 + -2w + -1w2 = -15 + 8w + 2w2 + 15 + -8w + -2w2

Reorder the terms:
24 + -2w + -1w2 = -15 + 15 + 8w + -8w + 2w2 + -2w2

Combine like terms: -15 + 15 = 0
24 + -2w + -1w2 = 0 + 8w + -8w + 2w2 + -2w2
24 + -2w + -1w2 = 8w + -8w + 2w2 + -2w2

Combine like terms: 8w + -8w = 0
24 + -2w + -1w2 = 0 + 2w2 + -2w2
24 + -2w + -1w2 = 2w2 + -2w2

Combine like terms: 2w2 + -2w2 = 0
24 + -2w + -1w2 = 0

Factor a trinomial.
(4 + -1w)(6 + w) = 0


Subproblem 1
Set the factor '(4 + -1w)' equal to zero and attempt to solve:

Simplifying
4 + -1w = 0

Solving
4 + -1w = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1w = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1w = 0 + -4
-1w = 0 + -4

Combine like terms: 0 + -4 = -4
-1w = -4

Divide each side by '-1'.
w = 4

Simplifying
w = 4

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 = {4, -6}

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