2w^2+24w+73=w+7

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Solution for 2w^2+24w+73=w+7 equation: 


Simplifying
2w2 + 24w + 73 = w + 7

Reorder the terms:
73 + 24w + 2w2 = w + 7

Reorder the terms:
73 + 24w + 2w2 = 7 + w

Solving
73 + 24w + 2w2 = 7 + w

Solving for variable 'w'.

Reorder the terms:
73 + -7 + 24w + -1w + 2w2 = 7 + w + -7 + -1w

Combine like terms: 73 + -7 = 66
66 + 24w + -1w + 2w2 = 7 + w + -7 + -1w

Combine like terms: 24w + -1w = 23w
66 + 23w + 2w2 = 7 + w + -7 + -1w

Reorder the terms:
66 + 23w + 2w2 = 7 + -7 + w + -1w

Combine like terms: 7 + -7 = 0
66 + 23w + 2w2 = 0 + w + -1w
66 + 23w + 2w2 = w + -1w

Combine like terms: w + -1w = 0
66 + 23w + 2w2 = 0

Factor a trinomial.
(6 + w)(11 + 2w) = 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 '(11 + 2w)' equal to zero and attempt to solve:

Simplifying
11 + 2w = 0

Solving
11 + 2w = 0

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

Add '-11' to each side of the equation.
11 + -11 + 2w = 0 + -11

Combine like terms: 11 + -11 = 0
0 + 2w = 0 + -11
2w = 0 + -11

Combine like terms: 0 + -11 = -11
2w = -11

Divide each side by '2'.
w = -5.5

Simplifying
w = -5.5
Solution
w = {-6, -5.5}

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