2w^2+16w+18=w^2+10w+25

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Solution for 2w^2+16w+18=w^2+10w+25 equation: 


Simplifying
2w2 + 16w + 18 = w2 + 10w + 25

Reorder the terms:
18 + 16w + 2w2 = w2 + 10w + 25

Reorder the terms:
18 + 16w + 2w2 = 25 + 10w + w2

Solving
18 + 16w + 2w2 = 25 + 10w + w2

Solving for variable 'w'.

Reorder the terms:
18 + -25 + 16w + -10w + 2w2 + -1w2 = 25 + 10w + w2 + -25 + -10w + -1w2

Combine like terms: 18 + -25 = -7
-7 + 16w + -10w + 2w2 + -1w2 = 25 + 10w + w2 + -25 + -10w + -1w2

Combine like terms: 16w + -10w = 6w
-7 + 6w + 2w2 + -1w2 = 25 + 10w + w2 + -25 + -10w + -1w2

Combine like terms: 2w2 + -1w2 = 1w2
-7 + 6w + 1w2 = 25 + 10w + w2 + -25 + -10w + -1w2

Reorder the terms:
-7 + 6w + 1w2 = 25 + -25 + 10w + -10w + w2 + -1w2

Combine like terms: 25 + -25 = 0
-7 + 6w + 1w2 = 0 + 10w + -10w + w2 + -1w2
-7 + 6w + 1w2 = 10w + -10w + w2 + -1w2

Combine like terms: 10w + -10w = 0
-7 + 6w + 1w2 = 0 + w2 + -1w2
-7 + 6w + 1w2 = w2 + -1w2

Combine like terms: w2 + -1w2 = 0
-7 + 6w + 1w2 = 0

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


Subproblem 1
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

Subproblem 2
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
Solution
w = {-7, 1}

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