(w-4)(w-4)=2w^2-2w+9

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Solution for (w-4)(w-4)=2w^2-2w+9 equation: 


Simplifying
(w + -4)(w + -4) = 2w2 + -2w + 9

Reorder the terms:
(-4 + w)(w + -4) = 2w2 + -2w + 9

Reorder the terms:
(-4 + w)(-4 + w) = 2w2 + -2w + 9

Multiply (-4 + w) * (-4 + w)
(-4(-4 + w) + w(-4 + w)) = 2w2 + -2w + 9
((-4 * -4 + w * -4) + w(-4 + w)) = 2w2 + -2w + 9
((16 + -4w) + w(-4 + w)) = 2w2 + -2w + 9
(16 + -4w + (-4 * w + w * w)) = 2w2 + -2w + 9
(16 + -4w + (-4w + w2)) = 2w2 + -2w + 9

Combine like terms: -4w + -4w = -8w
(16 + -8w + w2) = 2w2 + -2w + 9

Reorder the terms:
16 + -8w + w2 = 9 + -2w + 2w2

Solving
16 + -8w + w2 = 9 + -2w + 2w2

Solving for variable 'w'.

Reorder the terms:
16 + -9 + -8w + 2w + w2 + -2w2 = 9 + -2w + 2w2 + -9 + 2w + -2w2

Combine like terms: 16 + -9 = 7
7 + -8w + 2w + w2 + -2w2 = 9 + -2w + 2w2 + -9 + 2w + -2w2

Combine like terms: -8w + 2w = -6w
7 + -6w + w2 + -2w2 = 9 + -2w + 2w2 + -9 + 2w + -2w2

Combine like terms: w2 + -2w2 = -1w2
7 + -6w + -1w2 = 9 + -2w + 2w2 + -9 + 2w + -2w2

Reorder the terms:
7 + -6w + -1w2 = 9 + -9 + -2w + 2w + 2w2 + -2w2

Combine like terms: 9 + -9 = 0
7 + -6w + -1w2 = 0 + -2w + 2w + 2w2 + -2w2
7 + -6w + -1w2 = -2w + 2w + 2w2 + -2w2

Combine like terms: -2w + 2w = 0
7 + -6w + -1w2 = 0 + 2w2 + -2w2
7 + -6w + -1w2 = 2w2 + -2w2

Combine like terms: 2w2 + -2w2 = 0
7 + -6w + -1w2 = 0

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


Subproblem 1
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

Subproblem 2
Set the factor '(7 + w)' equal to zero and attempt to solve:

Simplifying
7 + w = 0

Solving
7 + w = 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 + w = 0 + -7

Combine like terms: 7 + -7 = 0
0 + w = 0 + -7
w = 0 + -7

Combine like terms: 0 + -7 = -7
w = -7

Simplifying
w = -7
Solution
w = {1, -7}

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