3w+55=w^2+10w+25

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Solution for 3w+55=w^2+10w+25 equation: 


Simplifying
3w + 55 = w2 + 10w + 25

Reorder the terms:
55 + 3w = w2 + 10w + 25

Reorder the terms:
55 + 3w = 25 + 10w + w2

Solving
55 + 3w = 25 + 10w + w2

Solving for variable 'w'.

Reorder the terms:
55 + -25 + 3w + -10w + -1w2 = 25 + 10w + w2 + -25 + -10w + -1w2

Combine like terms: 55 + -25 = 30
30 + 3w + -10w + -1w2 = 25 + 10w + w2 + -25 + -10w + -1w2

Combine like terms: 3w + -10w = -7w
30 + -7w + -1w2 = 25 + 10w + w2 + -25 + -10w + -1w2

Reorder the terms:
30 + -7w + -1w2 = 25 + -25 + 10w + -10w + w2 + -1w2

Combine like terms: 25 + -25 = 0
30 + -7w + -1w2 = 0 + 10w + -10w + w2 + -1w2
30 + -7w + -1w2 = 10w + -10w + w2 + -1w2

Combine like terms: 10w + -10w = 0
30 + -7w + -1w2 = 0 + w2 + -1w2
30 + -7w + -1w2 = w2 + -1w2

Combine like terms: w2 + -1w2 = 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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