2w^2-9w+19=(w-5)(w-5)

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Solution for 2w^2-9w+19=(w-5)(w-5) equation: 


Simplifying
2w2 + -9w + 19 = (w + -5)(w + -5)

Reorder the terms:
19 + -9w + 2w2 = (w + -5)(w + -5)

Reorder the terms:
19 + -9w + 2w2 = (-5 + w)(w + -5)

Reorder the terms:
19 + -9w + 2w2 = (-5 + w)(-5 + w)

Multiply (-5 + w) * (-5 + w)
19 + -9w + 2w2 = (-5(-5 + w) + w(-5 + w))
19 + -9w + 2w2 = ((-5 * -5 + w * -5) + w(-5 + w))
19 + -9w + 2w2 = ((25 + -5w) + w(-5 + w))
19 + -9w + 2w2 = (25 + -5w + (-5 * w + w * w))
19 + -9w + 2w2 = (25 + -5w + (-5w + w2))

Combine like terms: -5w + -5w = -10w
19 + -9w + 2w2 = (25 + -10w + w2)

Solving
19 + -9w + 2w2 = 25 + -10w + w2

Solving for variable 'w'.

Reorder the terms:
19 + -25 + -9w + 10w + 2w2 + -1w2 = 25 + -10w + w2 + -25 + 10w + -1w2

Combine like terms: 19 + -25 = -6
-6 + -9w + 10w + 2w2 + -1w2 = 25 + -10w + w2 + -25 + 10w + -1w2

Combine like terms: -9w + 10w = 1w
-6 + 1w + 2w2 + -1w2 = 25 + -10w + w2 + -25 + 10w + -1w2

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

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

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

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

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

Factor a trinomial.
(-3 + -1w)(2 + -1w) = 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 '(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
Solution
w = {-3, 2}

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