2w^2-17w=-26

Solution for 2w^2-17w=-26 equation:

Simplifying
2w2 + -17w = -26

Reorder the terms:
-17w + 2w2 = -26

Solving
-17w + 2w2 = -26

Solving for variable 'w'.

Reorder the terms:
26 + -17w + 2w2 = -26 + 26

Combine like terms: -26 + 26 = 0
26 + -17w + 2w2 = 0

Factor a trinomial.
(2 + -1w)(13 + -2w) = 0

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

Simplifying
2 + -1w = 0

Solving
2 + -1w = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1w = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1w = 0 + -2
-1w = 0 + -2

Combine like terms: 0 + -2 = -2
-1w = -2

Divide each side by '-1'.
w = 2

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

Simplifying
13 + -2w = 0

Solving
13 + -2w = 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 + -2w = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -2w = 0 + -13
-2w = 0 + -13

Combine like terms: 0 + -13 = -13
-2w = -13

Divide each side by '-2'.
w = 6.5

Simplifying
w = 6.5
Solution
w = {2, 6.5}