w(w-7)=78

Solution for w(w-7)=78 equation:

Simplifying
w(w + -7) = 78

Reorder the terms:
w(-7 + w) = 78
(-7 * w + w * w) = 78
(-7w + w2) = 78

Solving
-7w + w2 = 78

Solving for variable 'w'.

Reorder the terms:
-78 + -7w + w2 = 78 + -78

Combine like terms: 78 + -78 = 0
-78 + -7w + w2 = 0

Factor a trinomial.
(-6 + -1w)(13 + -1w) = 0

Subproblem 1
Set the factor '(-6 + -1w)' equal to zero and attempt to solve:

Simplifying
-6 + -1w = 0

Solving
-6 + -1w = 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 + -1w = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1w = 0 + 6
-1w = 0 + 6

Combine like terms: 0 + 6 = 6
-1w = 6

Divide each side by '-1'.
w = -6

Simplifying
w = -6
Subproblem 2
Set the factor '(13 + -1w)' equal to zero and attempt to solve:

Simplifying
13 + -1w = 0

Solving
13 + -1w = 0

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

Add '-13' to each side of the equation.
13 + -13 + -1w = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -1w = 0 + -13
-1w = 0 + -13

Combine like terms: 0 + -13 = -13
-1w = -13

Divide each side by '-1'.
w = 13

Simplifying
w = 13
Solution
w = {-6, 13}