2w^2+3w+29=w^2-6w+9

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Solution for 2w^2+3w+29=w^2-6w+9 equation: 


Simplifying
2w2 + 3w + 29 = w2 + -6w + 9

Reorder the terms:
29 + 3w + 2w2 = w2 + -6w + 9

Reorder the terms:
29 + 3w + 2w2 = 9 + -6w + w2

Solving
29 + 3w + 2w2 = 9 + -6w + w2

Solving for variable 'w'.

Reorder the terms:
29 + -9 + 3w + 6w + 2w2 + -1w2 = 9 + -6w + w2 + -9 + 6w + -1w2

Combine like terms: 29 + -9 = 20
20 + 3w + 6w + 2w2 + -1w2 = 9 + -6w + w2 + -9 + 6w + -1w2

Combine like terms: 3w + 6w = 9w
20 + 9w + 2w2 + -1w2 = 9 + -6w + w2 + -9 + 6w + -1w2

Combine like terms: 2w2 + -1w2 = 1w2
20 + 9w + 1w2 = 9 + -6w + w2 + -9 + 6w + -1w2

Reorder the terms:
20 + 9w + 1w2 = 9 + -9 + -6w + 6w + w2 + -1w2

Combine like terms: 9 + -9 = 0
20 + 9w + 1w2 = 0 + -6w + 6w + w2 + -1w2
20 + 9w + 1w2 = -6w + 6w + w2 + -1w2

Combine like terms: -6w + 6w = 0
20 + 9w + 1w2 = 0 + w2 + -1w2
20 + 9w + 1w2 = w2 + -1w2

Combine like terms: w2 + -1w2 = 0
20 + 9w + 1w2 = 0

Factor a trinomial.
(5 + w)(4 + w) = 0


Subproblem 1
Set the factor '(5 + w)' equal to zero and attempt to solve:

Simplifying
5 + w = 0

Solving
5 + w = 0

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

Add '-5' to each side of the equation.
5 + -5 + w = 0 + -5

Combine like terms: 5 + -5 = 0
0 + w = 0 + -5
w = 0 + -5

Combine like terms: 0 + -5 = -5
w = -5

Simplifying
w = -5

Subproblem 2
Set the factor '(4 + w)' equal to zero and attempt to solve:

Simplifying
4 + w = 0

Solving
4 + w = 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 + w = 0 + -4

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

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

Simplifying
w = -4
Solution
w = {-5, -4}

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