2y^2=-y+10

Solution for 2y^2=-y+10 equation:

Simplifying
2y2 = -1y + 10

Reorder the terms:
2y2 = 10 + -1y

Solving
2y2 = 10 + -1y

Solving for variable 'y'.

Reorder the terms:
-10 + y + 2y2 = 10 + -1y + -10 + y

Reorder the terms:
-10 + y + 2y2 = 10 + -10 + -1y + y

Combine like terms: 10 + -10 = 0
-10 + y + 2y2 = 0 + -1y + y
-10 + y + 2y2 = -1y + y

Combine like terms: -1y + y = 0
-10 + y + 2y2 = 0

Factor a trinomial.
(-5 + -2y)(2 + -1y) = 0

Subproblem 1
Set the factor '(-5 + -2y)' equal to zero and attempt to solve:

Simplifying
-5 + -2y = 0

Solving
-5 + -2y = 0

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

Add '5' to each side of the equation.
-5 + 5 + -2y = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -2y = 0 + 5
-2y = 0 + 5

Combine like terms: 0 + 5 = 5
-2y = 5

Divide each side by '-2'.
y = -2.5

Simplifying
y = -2.5
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 = {-2.5, 2}