2w^2-11w+14=w^2-4w+4

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Solution for 2w^2-11w+14=w^2-4w+4 equation: 


Simplifying
2w2 + -11w + 14 = w2 + -4w + 4

Reorder the terms:
14 + -11w + 2w2 = w2 + -4w + 4

Reorder the terms:
14 + -11w + 2w2 = 4 + -4w + w2

Solving
14 + -11w + 2w2 = 4 + -4w + w2

Solving for variable 'w'.

Reorder the terms:
14 + -4 + -11w + 4w + 2w2 + -1w2 = 4 + -4w + w2 + -4 + 4w + -1w2

Combine like terms: 14 + -4 = 10
10 + -11w + 4w + 2w2 + -1w2 = 4 + -4w + w2 + -4 + 4w + -1w2

Combine like terms: -11w + 4w = -7w
10 + -7w + 2w2 + -1w2 = 4 + -4w + w2 + -4 + 4w + -1w2

Combine like terms: 2w2 + -1w2 = 1w2
10 + -7w + 1w2 = 4 + -4w + w2 + -4 + 4w + -1w2

Reorder the terms:
10 + -7w + 1w2 = 4 + -4 + -4w + 4w + w2 + -1w2

Combine like terms: 4 + -4 = 0
10 + -7w + 1w2 = 0 + -4w + 4w + w2 + -1w2
10 + -7w + 1w2 = -4w + 4w + w2 + -1w2

Combine like terms: -4w + 4w = 0
10 + -7w + 1w2 = 0 + w2 + -1w2
10 + -7w + 1w2 = w2 + -1w2

Combine like terms: w2 + -1w2 = 0
10 + -7w + 1w2 = 0

Factor a trinomial.
(2 + -1w)(5 + -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 '(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 = {2, 5}

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