w^2-6w+9=-4w+72

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Solution for w^2-6w+9=-4w+72 equation: 


Simplifying
w2 + -6w + 9 = -4w + 72

Reorder the terms:
9 + -6w + w2 = -4w + 72

Reorder the terms:
9 + -6w + w2 = 72 + -4w

Solving
9 + -6w + w2 = 72 + -4w

Solving for variable 'w'.

Reorder the terms:
9 + -72 + -6w + 4w + w2 = 72 + -4w + -72 + 4w

Combine like terms: 9 + -72 = -63
-63 + -6w + 4w + w2 = 72 + -4w + -72 + 4w

Combine like terms: -6w + 4w = -2w
-63 + -2w + w2 = 72 + -4w + -72 + 4w

Reorder the terms:
-63 + -2w + w2 = 72 + -72 + -4w + 4w

Combine like terms: 72 + -72 = 0
-63 + -2w + w2 = 0 + -4w + 4w
-63 + -2w + w2 = -4w + 4w

Combine like terms: -4w + 4w = 0
-63 + -2w + w2 = 0

Factor a trinomial.
(-7 + -1w)(9 + -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 '(9 + -1w)' equal to zero and attempt to solve:

Simplifying
9 + -1w = 0

Solving
9 + -1w = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1w = 0 + -9

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

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

Divide each side by '-1'.
w = 9

Simplifying
w = 9
Solution
w = {-7, 9}

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