2y^2-y-5=1

Solution for 2y^2-y-5=1 equation:

Simplifying
2y2 + -1y + -5 = 1

Reorder the terms:
-5 + -1y + 2y2 = 1

Solving
-5 + -1y + 2y2 = 1

Solving for variable 'y'.

Reorder the terms:
-5 + -1 + -1y + 2y2 = 1 + -1

Combine like terms: -5 + -1 = -6
-6 + -1y + 2y2 = 1 + -1

Combine like terms: 1 + -1 = 0
-6 + -1y + 2y2 = 0

Factor a trinomial.
(-3 + -2y)(2 + -1y) = 0

Subproblem 1
Set the factor '(-3 + -2y)' equal to zero and attempt to solve:

Simplifying
-3 + -2y = 0

Solving
-3 + -2y = 0

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

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

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

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

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

Simplifying
y = -1.5
Subproblem 2
Set the factor '(2 + -1y)' equal to zero and attempt to solve:

Simplifying
2 + -1y = 0

Solving
2 + -1y = 0

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

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

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

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

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

Simplifying
y = 2
Solution
y = {-1.5, 2}