2w^2-16w=12w-48

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Solution for 2w^2-16w=12w-48 equation: 


Simplifying
2w2 + -16w = 12w + -48

Reorder the terms:
-16w + 2w2 = 12w + -48

Reorder the terms:
-16w + 2w2 = -48 + 12w

Solving
-16w + 2w2 = -48 + 12w

Solving for variable 'w'.

Reorder the terms:
48 + -16w + -12w + 2w2 = -48 + 12w + 48 + -12w

Combine like terms: -16w + -12w = -28w
48 + -28w + 2w2 = -48 + 12w + 48 + -12w

Reorder the terms:
48 + -28w + 2w2 = -48 + 48 + 12w + -12w

Combine like terms: -48 + 48 = 0
48 + -28w + 2w2 = 0 + 12w + -12w
48 + -28w + 2w2 = 12w + -12w

Combine like terms: 12w + -12w = 0
48 + -28w + 2w2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(24 + -14w + w2) = 0

Factor a trinomial.
2((2 + -1w)(12 + -1w)) = 0

Ignore the factor 2.

Subproblem 1
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

Subproblem 2
Set the factor '(12 + -1w)' equal to zero and attempt to solve:

Simplifying
12 + -1w = 0

Solving
12 + -1w = 0

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

Add '-12' to each side of the equation.
12 + -12 + -1w = 0 + -12

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

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

Divide each side by '-1'.
w = 12

Simplifying
w = 12
Solution
w = {2, 12}

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