(4+w)(w)=77

Solution for (4+w)(w)=77 equation:

Simplifying
(4 + w)(w) = 77

Reorder the terms for easier multiplication:
w(4 + w) = 77
(4 * w + w * w) = 77
(4w + w2) = 77

Solving
4w + w2 = 77

Solving for variable 'w'.

Reorder the terms:
-77 + 4w + w2 = 77 + -77

Combine like terms: 77 + -77 = 0
-77 + 4w + w2 = 0

Factor a trinomial.
(-11 + -1w)(7 + -1w) = 0

Subproblem 1
Set the factor '(-11 + -1w)' equal to zero and attempt to solve:

Simplifying
-11 + -1w = 0

Solving
-11 + -1w = 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 + -1w = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -1w = 0 + 11
-1w = 0 + 11

Combine like terms: 0 + 11 = 11
-1w = 11

Divide each side by '-1'.
w = -11

Simplifying
w = -11
Subproblem 2
Set the factor '(7 + -1w)' equal to zero and attempt to solve:

Simplifying
7 + -1w = 0

Solving
7 + -1w = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1w = 0 + -7

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

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

Divide each side by '-1'.
w = 7

Simplifying
w = 7
Solution
w = {-11, 7}