(w-3)(w-3)=9+2w

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Solution for (w-3)(w-3)=9+2w equation: 


Simplifying
(w + -3)(w + -3) = 9 + 2w

Reorder the terms:
(-3 + w)(w + -3) = 9 + 2w

Reorder the terms:
(-3 + w)(-3 + w) = 9 + 2w

Multiply (-3 + w) * (-3 + w)
(-3(-3 + w) + w(-3 + w)) = 9 + 2w
((-3 * -3 + w * -3) + w(-3 + w)) = 9 + 2w
((9 + -3w) + w(-3 + w)) = 9 + 2w
(9 + -3w + (-3 * w + w * w)) = 9 + 2w
(9 + -3w + (-3w + w2)) = 9 + 2w

Combine like terms: -3w + -3w = -6w
(9 + -6w + w2) = 9 + 2w

Add '-9' to each side of the equation.
9 + -6w + -9 + w2 = 9 + -9 + 2w

Reorder the terms:
9 + -9 + -6w + w2 = 9 + -9 + 2w

Combine like terms: 9 + -9 = 0
0 + -6w + w2 = 9 + -9 + 2w
-6w + w2 = 9 + -9 + 2w

Combine like terms: 9 + -9 = 0
-6w + w2 = 0 + 2w
-6w + w2 = 2w

Solving
-6w + w2 = 2w

Solving for variable 'w'.

Reorder the terms:
-6w + -2w + w2 = 2w + -2w

Combine like terms: -6w + -2w = -8w
-8w + w2 = 2w + -2w

Combine like terms: 2w + -2w = 0
-8w + w2 = 0

Factor out the Greatest Common Factor (GCF), 'w'.
w(-8 + w) = 0


Subproblem 1
Set the factor 'w' equal to zero and attempt to solve:

Simplifying
w = 0

Solving
w = 0

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

Simplifying
w = 0

Subproblem 2
Set the factor '(-8 + w)' equal to zero and attempt to solve:

Simplifying
-8 + w = 0

Solving
-8 + w = 0

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

Add '8' to each side of the equation.
-8 + 8 + w = 0 + 8

Combine like terms: -8 + 8 = 0
0 + w = 0 + 8
w = 0 + 8

Combine like terms: 0 + 8 = 8
w = 8

Simplifying
w = 8
Solution
w = {0, 8}

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