5w^2-6w=-1

Solution for 5w^2-6w=-1 equation:

Simplifying
5w2 + -6w = -1

Reorder the terms:
-6w + 5w2 = -1

Solving
-6w + 5w2 = -1

Solving for variable 'w'.

Reorder the terms:
1 + -6w + 5w2 = -1 + 1

Combine like terms: -1 + 1 = 0
1 + -6w + 5w2 = 0

Factor a trinomial.
(1 + -5w)(1 + -1w) = 0

Subproblem 1
Set the factor '(1 + -5w)' equal to zero and attempt to solve:

Simplifying
1 + -5w = 0

Solving
1 + -5w = 0

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

Add '-1' to each side of the equation.
1 + -1 + -5w = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -5w = 0 + -1
-5w = 0 + -1

Combine like terms: 0 + -1 = -1
-5w = -1

Divide each side by '-5'.
w = 0.2

Simplifying
w = 0.2
Subproblem 2
Set the factor '(1 + -1w)' equal to zero and attempt to solve:

Simplifying
1 + -1w = 0

Solving
1 + -1w = 0

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

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

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

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

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

Simplifying
w = 1
Solution
w = {0.2, 1}