77=(4+w)(w)

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

Simplifying
77 = (4 + w)(w)

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

Solving
77 = 4w + w2

Solving for variable 'w'.

Reorder the terms:
77 + -4w + -1w2 = 4w + -4w + w2 + -1w2

Combine like terms: 4w + -4w = 0
77 + -4w + -1w2 = 0 + w2 + -1w2
77 + -4w + -1w2 = w2 + -1w2

Combine like terms: w2 + -1w2 = 0
77 + -4w + -1w2 = 0

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

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

Simplifying
11 + w = 0

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

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

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

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