2w^2-13w+24=(w-2)(w-2)

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Solution for 2w^2-13w+24=(w-2)(w-2) equation: 


Simplifying
2w2 + -13w + 24 = (w + -2)(w + -2)

Reorder the terms:
24 + -13w + 2w2 = (w + -2)(w + -2)

Reorder the terms:
24 + -13w + 2w2 = (-2 + w)(w + -2)

Reorder the terms:
24 + -13w + 2w2 = (-2 + w)(-2 + w)

Multiply (-2 + w) * (-2 + w)
24 + -13w + 2w2 = (-2(-2 + w) + w(-2 + w))
24 + -13w + 2w2 = ((-2 * -2 + w * -2) + w(-2 + w))
24 + -13w + 2w2 = ((4 + -2w) + w(-2 + w))
24 + -13w + 2w2 = (4 + -2w + (-2 * w + w * w))
24 + -13w + 2w2 = (4 + -2w + (-2w + w2))

Combine like terms: -2w + -2w = -4w
24 + -13w + 2w2 = (4 + -4w + w2)

Solving
24 + -13w + 2w2 = 4 + -4w + w2

Solving for variable 'w'.

Reorder the terms:
24 + -4 + -13w + 4w + 2w2 + -1w2 = 4 + -4w + w2 + -4 + 4w + -1w2

Combine like terms: 24 + -4 = 20
20 + -13w + 4w + 2w2 + -1w2 = 4 + -4w + w2 + -4 + 4w + -1w2

Combine like terms: -13w + 4w = -9w
20 + -9w + 2w2 + -1w2 = 4 + -4w + w2 + -4 + 4w + -1w2

Combine like terms: 2w2 + -1w2 = 1w2
20 + -9w + 1w2 = 4 + -4w + w2 + -4 + 4w + -1w2

Reorder the terms:
20 + -9w + 1w2 = 4 + -4 + -4w + 4w + w2 + -1w2

Combine like terms: 4 + -4 = 0
20 + -9w + 1w2 = 0 + -4w + 4w + w2 + -1w2
20 + -9w + 1w2 = -4w + 4w + w2 + -1w2

Combine like terms: -4w + 4w = 0
20 + -9w + 1w2 = 0 + w2 + -1w2
20 + -9w + 1w2 = w2 + -1w2

Combine like terms: w2 + -1w2 = 0
20 + -9w + 1w2 = 0

Factor a trinomial.
(4 + -1w)(5 + -1w) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(5 + -1w)' equal to zero and attempt to solve:

Simplifying
5 + -1w = 0

Solving
5 + -1w = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1w = 0 + -5

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

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

Divide each side by '-1'.
w = 5

Simplifying
w = 5
Solution
w = {4, 5}

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