(w-2)(w-2)=2w^2+6w+25

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Solution for (w-2)(w-2)=2w^2+6w+25 equation: 


Simplifying
(w + -2)(w + -2) = 2w2 + 6w + 25

Reorder the terms:
(-2 + w)(w + -2) = 2w2 + 6w + 25

Reorder the terms:
(-2 + w)(-2 + w) = 2w2 + 6w + 25

Multiply (-2 + w) * (-2 + w)
(-2(-2 + w) + w(-2 + w)) = 2w2 + 6w + 25
((-2 * -2 + w * -2) + w(-2 + w)) = 2w2 + 6w + 25
((4 + -2w) + w(-2 + w)) = 2w2 + 6w + 25
(4 + -2w + (-2 * w + w * w)) = 2w2 + 6w + 25
(4 + -2w + (-2w + w2)) = 2w2 + 6w + 25

Combine like terms: -2w + -2w = -4w
(4 + -4w + w2) = 2w2 + 6w + 25

Reorder the terms:
4 + -4w + w2 = 25 + 6w + 2w2

Solving
4 + -4w + w2 = 25 + 6w + 2w2

Solving for variable 'w'.

Reorder the terms:
4 + -25 + -4w + -6w + w2 + -2w2 = 25 + 6w + 2w2 + -25 + -6w + -2w2

Combine like terms: 4 + -25 = -21
-21 + -4w + -6w + w2 + -2w2 = 25 + 6w + 2w2 + -25 + -6w + -2w2

Combine like terms: -4w + -6w = -10w
-21 + -10w + w2 + -2w2 = 25 + 6w + 2w2 + -25 + -6w + -2w2

Combine like terms: w2 + -2w2 = -1w2
-21 + -10w + -1w2 = 25 + 6w + 2w2 + -25 + -6w + -2w2

Reorder the terms:
-21 + -10w + -1w2 = 25 + -25 + 6w + -6w + 2w2 + -2w2

Combine like terms: 25 + -25 = 0
-21 + -10w + -1w2 = 0 + 6w + -6w + 2w2 + -2w2
-21 + -10w + -1w2 = 6w + -6w + 2w2 + -2w2

Combine like terms: 6w + -6w = 0
-21 + -10w + -1w2 = 0 + 2w2 + -2w2
-21 + -10w + -1w2 = 2w2 + -2w2

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

Factor out the Greatest Common Factor (GCF), '-1'.
-1(21 + 10w + w2) = 0

Factor a trinomial.
-1((7 + w)(3 + w)) = 0

Ignore the factor -1.

Subproblem 1
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

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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