2w^2+16w+24=w^2+12w+36

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Solution for 2w^2+16w+24=w^2+12w+36 equation: 


Simplifying
2w2 + 16w + 24 = w2 + 12w + 36

Reorder the terms:
24 + 16w + 2w2 = w2 + 12w + 36

Reorder the terms:
24 + 16w + 2w2 = 36 + 12w + w2

Solving
24 + 16w + 2w2 = 36 + 12w + w2

Solving for variable 'w'.

Reorder the terms:
24 + -36 + 16w + -12w + 2w2 + -1w2 = 36 + 12w + w2 + -36 + -12w + -1w2

Combine like terms: 24 + -36 = -12
-12 + 16w + -12w + 2w2 + -1w2 = 36 + 12w + w2 + -36 + -12w + -1w2

Combine like terms: 16w + -12w = 4w
-12 + 4w + 2w2 + -1w2 = 36 + 12w + w2 + -36 + -12w + -1w2

Combine like terms: 2w2 + -1w2 = 1w2
-12 + 4w + 1w2 = 36 + 12w + w2 + -36 + -12w + -1w2

Reorder the terms:
-12 + 4w + 1w2 = 36 + -36 + 12w + -12w + w2 + -1w2

Combine like terms: 36 + -36 = 0
-12 + 4w + 1w2 = 0 + 12w + -12w + w2 + -1w2
-12 + 4w + 1w2 = 12w + -12w + w2 + -1w2

Combine like terms: 12w + -12w = 0
-12 + 4w + 1w2 = 0 + w2 + -1w2
-12 + 4w + 1w2 = w2 + -1w2

Combine like terms: w2 + -1w2 = 0
-12 + 4w + 1w2 = 0

Factor a trinomial.
(-6 + -1w)(2 + -1w) = 0


Subproblem 1
Set the factor '(-6 + -1w)' equal to zero and attempt to solve:

Simplifying
-6 + -1w = 0

Solving
-6 + -1w = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1w = 0 + 6

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

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

Divide each side by '-1'.
w = -6

Simplifying
w = -6

Subproblem 2
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
Solution
w = {-6, 2}

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