w^2+9=2w^2+7w-21

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Solution for w^2+9=2w^2+7w-21 equation: 


Simplifying
w2 + 9 = 2w2 + 7w + -21

Reorder the terms:
9 + w2 = 2w2 + 7w + -21

Reorder the terms:
9 + w2 = -21 + 7w + 2w2

Solving
9 + w2 = -21 + 7w + 2w2

Solving for variable 'w'.

Reorder the terms:
9 + 21 + -7w + w2 + -2w2 = -21 + 7w + 2w2 + 21 + -7w + -2w2

Combine like terms: 9 + 21 = 30
30 + -7w + w2 + -2w2 = -21 + 7w + 2w2 + 21 + -7w + -2w2

Combine like terms: w2 + -2w2 = -1w2
30 + -7w + -1w2 = -21 + 7w + 2w2 + 21 + -7w + -2w2

Reorder the terms:
30 + -7w + -1w2 = -21 + 21 + 7w + -7w + 2w2 + -2w2

Combine like terms: -21 + 21 = 0
30 + -7w + -1w2 = 0 + 7w + -7w + 2w2 + -2w2
30 + -7w + -1w2 = 7w + -7w + 2w2 + -2w2

Combine like terms: 7w + -7w = 0
30 + -7w + -1w2 = 0 + 2w2 + -2w2
30 + -7w + -1w2 = 2w2 + -2w2

Combine like terms: 2w2 + -2w2 = 0
30 + -7w + -1w2 = 0

Factor a trinomial.
(3 + -1w)(10 + w) = 0


Subproblem 1
Set the factor '(3 + -1w)' equal to zero and attempt to solve:

Simplifying
3 + -1w = 0

Solving
3 + -1w = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1w = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1w = 0 + -3
-1w = 0 + -3

Combine like terms: 0 + -3 = -3
-1w = -3

Divide each side by '-1'.
w = 3

Simplifying
w = 3

Subproblem 2
Set the factor '(10 + w)' equal to zero and attempt to solve:

Simplifying
10 + w = 0

Solving
10 + w = 0

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

Add '-10' to each side of the equation.
10 + -10 + w = 0 + -10

Combine like terms: 10 + -10 = 0
0 + w = 0 + -10
w = 0 + -10

Combine like terms: 0 + -10 = -10
w = -10

Simplifying
w = -10
Solution
w = {3, -10}

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