2w^2+8w=-7w^2-3w+14

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Solution for 2w^2+8w=-7w^2-3w+14 equation: 


Simplifying
2w2 + 8w = -7w2 + -3w + 14

Reorder the terms:
8w + 2w2 = -7w2 + -3w + 14

Reorder the terms:
8w + 2w2 = 14 + -3w + -7w2

Solving
8w + 2w2 = 14 + -3w + -7w2

Solving for variable 'w'.

Reorder the terms:
-14 + 8w + 3w + 2w2 + 7w2 = 14 + -3w + -7w2 + -14 + 3w + 7w2

Combine like terms: 8w + 3w = 11w
-14 + 11w + 2w2 + 7w2 = 14 + -3w + -7w2 + -14 + 3w + 7w2

Combine like terms: 2w2 + 7w2 = 9w2
-14 + 11w + 9w2 = 14 + -3w + -7w2 + -14 + 3w + 7w2

Reorder the terms:
-14 + 11w + 9w2 = 14 + -14 + -3w + 3w + -7w2 + 7w2

Combine like terms: 14 + -14 = 0
-14 + 11w + 9w2 = 0 + -3w + 3w + -7w2 + 7w2
-14 + 11w + 9w2 = -3w + 3w + -7w2 + 7w2

Combine like terms: -3w + 3w = 0
-14 + 11w + 9w2 = 0 + -7w2 + 7w2
-14 + 11w + 9w2 = -7w2 + 7w2

Combine like terms: -7w2 + 7w2 = 0
-14 + 11w + 9w2 = 0

Factor a trinomial.
(-2 + -1w)(7 + -9w) = 0


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

Simplifying
-2 + -1w = 0

Solving
-2 + -1w = 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 + -1w = 0 + 2

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

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

Divide each side by '-1'.
w = -2

Simplifying
w = -2

Subproblem 2
Set the factor '(7 + -9w)' equal to zero and attempt to solve:

Simplifying
7 + -9w = 0

Solving
7 + -9w = 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 + -9w = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -9w = 0 + -7
-9w = 0 + -7

Combine like terms: 0 + -7 = -7
-9w = -7

Divide each side by '-9'.
w = 0.7777777778

Simplifying
w = 0.7777777778
Solution
w = {-2, 0.7777777778}

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