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

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


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

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

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

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

Solving for variable 'w'.

Reorder the terms:
-8 + 15 + -6w + -2w + 2w2 + -1w2 = -15 + 2w + w2 + 15 + -2w + -1w2

Combine like terms: -8 + 15 = 7
7 + -6w + -2w + 2w2 + -1w2 = -15 + 2w + w2 + 15 + -2w + -1w2

Combine like terms: -6w + -2w = -8w
7 + -8w + 2w2 + -1w2 = -15 + 2w + w2 + 15 + -2w + -1w2

Combine like terms: 2w2 + -1w2 = 1w2
7 + -8w + 1w2 = -15 + 2w + w2 + 15 + -2w + -1w2

Reorder the terms:
7 + -8w + 1w2 = -15 + 15 + 2w + -2w + w2 + -1w2

Combine like terms: -15 + 15 = 0
7 + -8w + 1w2 = 0 + 2w + -2w + w2 + -1w2
7 + -8w + 1w2 = 2w + -2w + w2 + -1w2

Combine like terms: 2w + -2w = 0
7 + -8w + 1w2 = 0 + w2 + -1w2
7 + -8w + 1w2 = w2 + -1w2

Combine like terms: w2 + -1w2 = 0
7 + -8w + 1w2 = 0

Factor a trinomial.
(1 + -1w)(7 + -1w) = 0


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

Simplifying
1 + -1w = 0

Solving
1 + -1w = 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 + -1w = 0 + -1

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

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

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

Simplifying
w = 1

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

Simplifying
7 + -1w = 0

Solving
7 + -1w = 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 + -1w = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1w = 0 + -7
-1w = 0 + -7

Combine like terms: 0 + -7 = -7
-1w = -7

Divide each side by '-1'.
w = 7

Simplifying
w = 7
Solution
w = {1, 7}

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