2w^2+13w-3=(w+5)(w+5)

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Solution for 2w^2+13w-3=(w+5)(w+5) equation: 


Simplifying
2w2 + 13w + -3 = (w + 5)(w + 5)

Reorder the terms:
-3 + 13w + 2w2 = (w + 5)(w + 5)

Reorder the terms:
-3 + 13w + 2w2 = (5 + w)(w + 5)

Reorder the terms:
-3 + 13w + 2w2 = (5 + w)(5 + w)

Multiply (5 + w) * (5 + w)
-3 + 13w + 2w2 = (5(5 + w) + w(5 + w))
-3 + 13w + 2w2 = ((5 * 5 + w * 5) + w(5 + w))
-3 + 13w + 2w2 = ((25 + 5w) + w(5 + w))
-3 + 13w + 2w2 = (25 + 5w + (5 * w + w * w))
-3 + 13w + 2w2 = (25 + 5w + (5w + w2))

Combine like terms: 5w + 5w = 10w
-3 + 13w + 2w2 = (25 + 10w + w2)

Solving
-3 + 13w + 2w2 = 25 + 10w + w2

Solving for variable 'w'.

Reorder the terms:
-3 + -25 + 13w + -10w + 2w2 + -1w2 = 25 + 10w + w2 + -25 + -10w + -1w2

Combine like terms: -3 + -25 = -28
-28 + 13w + -10w + 2w2 + -1w2 = 25 + 10w + w2 + -25 + -10w + -1w2

Combine like terms: 13w + -10w = 3w
-28 + 3w + 2w2 + -1w2 = 25 + 10w + w2 + -25 + -10w + -1w2

Combine like terms: 2w2 + -1w2 = 1w2
-28 + 3w + 1w2 = 25 + 10w + w2 + -25 + -10w + -1w2

Reorder the terms:
-28 + 3w + 1w2 = 25 + -25 + 10w + -10w + w2 + -1w2

Combine like terms: 25 + -25 = 0
-28 + 3w + 1w2 = 0 + 10w + -10w + w2 + -1w2
-28 + 3w + 1w2 = 10w + -10w + w2 + -1w2

Combine like terms: 10w + -10w = 0
-28 + 3w + 1w2 = 0 + w2 + -1w2
-28 + 3w + 1w2 = w2 + -1w2

Combine like terms: w2 + -1w2 = 0
-28 + 3w + 1w2 = 0

Factor a trinomial.
(-7 + -1w)(4 + -1w) = 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 '(4 + -1w)' equal to zero and attempt to solve:

Simplifying
4 + -1w = 0

Solving
4 + -1w = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1w = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1w = 0 + -4
-1w = 0 + -4

Combine like terms: 0 + -4 = -4
-1w = -4

Divide each side by '-1'.
w = 4

Simplifying
w = 4
Solution
w = {-7, 4}

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