4w^2+40w=69

Solution for 4w^2+40w=69 equation:

Simplifying
4w2 + 40w = 69

Reorder the terms:
40w + 4w2 = 69

Solving
40w + 4w2 = 69

Solving for variable 'w'.

Reorder the terms:
-69 + 40w + 4w2 = 69 + -69

Combine like terms: 69 + -69 = 0
-69 + 40w + 4w2 = 0

Factor a trinomial.
(-23 + -2w)(3 + -2w) = 0

Subproblem 1
Set the factor '(-23 + -2w)' equal to zero and attempt to solve:

Simplifying
-23 + -2w = 0

Solving
-23 + -2w = 0

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

Add '23' to each side of the equation.
-23 + 23 + -2w = 0 + 23

Combine like terms: -23 + 23 = 0
0 + -2w = 0 + 23
-2w = 0 + 23

Combine like terms: 0 + 23 = 23
-2w = 23

Divide each side by '-2'.
w = -11.5

Simplifying
w = -11.5
Subproblem 2
Set the factor '(3 + -2w)' equal to zero and attempt to solve:

Simplifying
3 + -2w = 0

Solving
3 + -2w = 0

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

Add '-3' to each side of the equation.
3 + -3 + -2w = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2w = 0 + -3
-2w = 0 + -3

Combine like terms: 0 + -3 = -3
-2w = -3

Divide each side by '-2'.
w = 1.5

Simplifying
w = 1.5
Solution
w = {-11.5, 1.5}