(w-3)(w-3)=2w^2-10w-12

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Solution for (w-3)(w-3)=2w^2-10w-12 equation: 


Simplifying
(w + -3)(w + -3) = 2w2 + -10w + -12

Reorder the terms:
(-3 + w)(w + -3) = 2w2 + -10w + -12

Reorder the terms:
(-3 + w)(-3 + w) = 2w2 + -10w + -12

Multiply (-3 + w) * (-3 + w)
(-3(-3 + w) + w(-3 + w)) = 2w2 + -10w + -12
((-3 * -3 + w * -3) + w(-3 + w)) = 2w2 + -10w + -12
((9 + -3w) + w(-3 + w)) = 2w2 + -10w + -12
(9 + -3w + (-3 * w + w * w)) = 2w2 + -10w + -12
(9 + -3w + (-3w + w2)) = 2w2 + -10w + -12

Combine like terms: -3w + -3w = -6w
(9 + -6w + w2) = 2w2 + -10w + -12

Reorder the terms:
9 + -6w + w2 = -12 + -10w + 2w2

Solving
9 + -6w + w2 = -12 + -10w + 2w2

Solving for variable 'w'.

Reorder the terms:
9 + 12 + -6w + 10w + w2 + -2w2 = -12 + -10w + 2w2 + 12 + 10w + -2w2

Combine like terms: 9 + 12 = 21
21 + -6w + 10w + w2 + -2w2 = -12 + -10w + 2w2 + 12 + 10w + -2w2

Combine like terms: -6w + 10w = 4w
21 + 4w + w2 + -2w2 = -12 + -10w + 2w2 + 12 + 10w + -2w2

Combine like terms: w2 + -2w2 = -1w2
21 + 4w + -1w2 = -12 + -10w + 2w2 + 12 + 10w + -2w2

Reorder the terms:
21 + 4w + -1w2 = -12 + 12 + -10w + 10w + 2w2 + -2w2

Combine like terms: -12 + 12 = 0
21 + 4w + -1w2 = 0 + -10w + 10w + 2w2 + -2w2
21 + 4w + -1w2 = -10w + 10w + 2w2 + -2w2

Combine like terms: -10w + 10w = 0
21 + 4w + -1w2 = 0 + 2w2 + -2w2
21 + 4w + -1w2 = 2w2 + -2w2

Combine like terms: 2w2 + -2w2 = 0
21 + 4w + -1w2 = 0

Factor a trinomial.
(7 + -1w)(3 + w) = 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 '(3 + w)' equal to zero and attempt to solve:

Simplifying
3 + w = 0

Solving
3 + w = 0

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

Add '-3' to each side of the equation.
3 + -3 + w = 0 + -3

Combine like terms: 3 + -3 = 0
0 + w = 0 + -3
w = 0 + -3

Combine like terms: 0 + -3 = -3
w = -3

Simplifying
w = -3
Solution
w = {7, -3}

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