(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.
(3 + -1w)(7 + w) = 0


Subproblem 1
Set the factor '(3 + -1w)' equal to zero and attempt to solve:

Simplifying
3 + -1w = 0

Solving
3 + -1w = 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 + -1w = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1w = 0 + -3
-1w = 0 + -3

Combine like terms: 0 + -3 = -3
-1w = -3

Divide each side by '-1'.
w = 3

Simplifying
w = 3

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 = {3, -7}

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