w(w+8)=825

Solution for w(w+8)=825 equation:

Simplifying
w(w + 8) = 825

Reorder the terms:
w(8 + w) = 825
(8 * w + w * w) = 825
(8w + w2) = 825

Solving
8w + w2 = 825

Solving for variable 'w'.

Reorder the terms:
-825 + 8w + w2 = 825 + -825

Combine like terms: 825 + -825 = 0
-825 + 8w + w2 = 0

Factor a trinomial.
(-33 + -1w)(25 + -1w) = 0

Subproblem 1
Set the factor '(-33 + -1w)' equal to zero and attempt to solve:

Simplifying
-33 + -1w = 0

Solving
-33 + -1w = 0

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

Add '33' to each side of the equation.
-33 + 33 + -1w = 0 + 33

Combine like terms: -33 + 33 = 0
0 + -1w = 0 + 33
-1w = 0 + 33

Combine like terms: 0 + 33 = 33
-1w = 33

Divide each side by '-1'.
w = -33

Simplifying
w = -33
Subproblem 2
Set the factor '(25 + -1w)' equal to zero and attempt to solve:

Simplifying
25 + -1w = 0

Solving
25 + -1w = 0

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

Add '-25' to each side of the equation.
25 + -25 + -1w = 0 + -25

Combine like terms: 25 + -25 = 0
0 + -1w = 0 + -25
-1w = 0 + -25

Combine like terms: 0 + -25 = -25
-1w = -25

Divide each side by '-1'.
w = 25

Simplifying
w = 25
Solution
w = {-33, 25}