(7w+9)(w+7)=47

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Solution for (7w+9)(w+7)=47 equation: 


Simplifying
(7w + 9)(w + 7) = 47

Reorder the terms:
(9 + 7w)(w + 7) = 47

Reorder the terms:
(9 + 7w)(7 + w) = 47

Multiply (9 + 7w) * (7 + w)
(9(7 + w) + 7w * (7 + w)) = 47
((7 * 9 + w * 9) + 7w * (7 + w)) = 47
((63 + 9w) + 7w * (7 + w)) = 47
(63 + 9w + (7 * 7w + w * 7w)) = 47
(63 + 9w + (49w + 7w2)) = 47

Combine like terms: 9w + 49w = 58w
(63 + 58w + 7w2) = 47

Solving
63 + 58w + 7w2 = 47

Solving for variable 'w'.

Reorder the terms:
63 + -47 + 58w + 7w2 = 47 + -47

Combine like terms: 63 + -47 = 16
16 + 58w + 7w2 = 47 + -47

Combine like terms: 47 + -47 = 0
16 + 58w + 7w2 = 0

Factor a trinomial.
(8 + w)(2 + 7w) = 0


Subproblem 1
Set the factor '(8 + w)' equal to zero and attempt to solve:

Simplifying
8 + w = 0

Solving
8 + w = 0

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

Add '-8' to each side of the equation.
8 + -8 + w = 0 + -8

Combine like terms: 8 + -8 = 0
0 + w = 0 + -8
w = 0 + -8

Combine like terms: 0 + -8 = -8
w = -8

Simplifying
w = -8

Subproblem 2
Set the factor '(2 + 7w)' equal to zero and attempt to solve:

Simplifying
2 + 7w = 0

Solving
2 + 7w = 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 + 7w = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 7w = 0 + -2
7w = 0 + -2

Combine like terms: 0 + -2 = -2
7w = -2

Divide each side by '7'.
w = -0.2857142857

Simplifying
w = -0.2857142857
Solution
w = {-8, -0.2857142857}

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