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

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


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

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

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

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

Multiply (-2 + w) * (-2 + w)
10 + 3w + 2w2 = (-2(-2 + w) + w(-2 + w))
10 + 3w + 2w2 = ((-2 * -2 + w * -2) + w(-2 + w))
10 + 3w + 2w2 = ((4 + -2w) + w(-2 + w))
10 + 3w + 2w2 = (4 + -2w + (-2 * w + w * w))
10 + 3w + 2w2 = (4 + -2w + (-2w + w2))

Combine like terms: -2w + -2w = -4w
10 + 3w + 2w2 = (4 + -4w + w2)

Solving
10 + 3w + 2w2 = 4 + -4w + w2

Solving for variable 'w'.

Reorder the terms:
10 + -4 + 3w + 4w + 2w2 + -1w2 = 4 + -4w + w2 + -4 + 4w + -1w2

Combine like terms: 10 + -4 = 6
6 + 3w + 4w + 2w2 + -1w2 = 4 + -4w + w2 + -4 + 4w + -1w2

Combine like terms: 3w + 4w = 7w
6 + 7w + 2w2 + -1w2 = 4 + -4w + w2 + -4 + 4w + -1w2

Combine like terms: 2w2 + -1w2 = 1w2
6 + 7w + 1w2 = 4 + -4w + w2 + -4 + 4w + -1w2

Reorder the terms:
6 + 7w + 1w2 = 4 + -4 + -4w + 4w + w2 + -1w2

Combine like terms: 4 + -4 = 0
6 + 7w + 1w2 = 0 + -4w + 4w + w2 + -1w2
6 + 7w + 1w2 = -4w + 4w + w2 + -1w2

Combine like terms: -4w + 4w = 0
6 + 7w + 1w2 = 0 + w2 + -1w2
6 + 7w + 1w2 = w2 + -1w2

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

Factor a trinomial.
(6 + w)(1 + w) = 0


Subproblem 1
Set the factor '(6 + w)' equal to zero and attempt to solve:

Simplifying
6 + w = 0

Solving
6 + w = 0

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

Add '-6' to each side of the equation.
6 + -6 + w = 0 + -6

Combine like terms: 6 + -6 = 0
0 + w = 0 + -6
w = 0 + -6

Combine like terms: 0 + -6 = -6
w = -6

Simplifying
w = -6

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

Simplifying
1 + w = 0

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

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

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

Simplifying
w = -1
Solution
w = {-6, -1}

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