2w^2-w-10=(w+2)(w+2)

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


Simplifying
2w2 + -1w + -10 = (w + 2)(w + 2)

Reorder the terms:
-10 + -1w + 2w2 = (w + 2)(w + 2)

Reorder the terms:
-10 + -1w + 2w2 = (2 + w)(w + 2)

Reorder the terms:
-10 + -1w + 2w2 = (2 + w)(2 + w)

Multiply (2 + w) * (2 + w)
-10 + -1w + 2w2 = (2(2 + w) + w(2 + w))
-10 + -1w + 2w2 = ((2 * 2 + w * 2) + w(2 + w))
-10 + -1w + 2w2 = ((4 + 2w) + w(2 + w))
-10 + -1w + 2w2 = (4 + 2w + (2 * w + w * w))
-10 + -1w + 2w2 = (4 + 2w + (2w + w2))

Combine like terms: 2w + 2w = 4w
-10 + -1w + 2w2 = (4 + 4w + w2)

Solving
-10 + -1w + 2w2 = 4 + 4w + w2

Solving for variable 'w'.

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

Combine like terms: -10 + -4 = -14
-14 + -1w + -4w + 2w2 + -1w2 = 4 + 4w + w2 + -4 + -4w + -1w2

Combine like terms: -1w + -4w = -5w
-14 + -5w + 2w2 + -1w2 = 4 + 4w + w2 + -4 + -4w + -1w2

Combine like terms: 2w2 + -1w2 = 1w2
-14 + -5w + 1w2 = 4 + 4w + w2 + -4 + -4w + -1w2

Reorder the terms:
-14 + -5w + 1w2 = 4 + -4 + 4w + -4w + w2 + -1w2

Combine like terms: 4 + -4 = 0
-14 + -5w + 1w2 = 0 + 4w + -4w + w2 + -1w2
-14 + -5w + 1w2 = 4w + -4w + w2 + -1w2

Combine like terms: 4w + -4w = 0
-14 + -5w + 1w2 = 0 + w2 + -1w2
-14 + -5w + 1w2 = w2 + -1w2

Combine like terms: w2 + -1w2 = 0
-14 + -5w + 1w2 = 0

Factor a trinomial.
(-2 + -1w)(7 + -1w) = 0


Subproblem 1
Set the factor '(-2 + -1w)' equal to zero and attempt to solve:

Simplifying
-2 + -1w = 0

Solving
-2 + -1w = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1w = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1w = 0 + 2
-1w = 0 + 2

Combine like terms: 0 + 2 = 2
-1w = 2

Divide each side by '-1'.
w = -2

Simplifying
w = -2

Subproblem 2
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
Solution
w = {-2, 7}

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