y+2y^2=105

Solution for y+2y^2=105 equation:

Simplifying
y + 2y2 = 105

Solving
y + 2y2 = 105

Solving for variable 'y'.

Reorder the terms:
-105 + y + 2y2 = 105 + -105

Combine like terms: 105 + -105 = 0
-105 + y + 2y2 = 0

Factor a trinomial.
(-15 + -2y)(7 + -1y) = 0

Subproblem 1
Set the factor '(-15 + -2y)' equal to zero and attempt to solve:

Simplifying
-15 + -2y = 0

Solving
-15 + -2y = 0

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

Add '15' to each side of the equation.
-15 + 15 + -2y = 0 + 15

Combine like terms: -15 + 15 = 0
0 + -2y = 0 + 15
-2y = 0 + 15

Combine like terms: 0 + 15 = 15
-2y = 15

Divide each side by '-2'.
y = -7.5

Simplifying
y = -7.5
Subproblem 2
Set the factor '(7 + -1y)' equal to zero and attempt to solve:

Simplifying
7 + -1y = 0

Solving
7 + -1y = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1y = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1y = 0 + -7
-1y = 0 + -7

Combine like terms: 0 + -7 = -7
-1y = -7

Divide each side by '-1'.
y = 7

Simplifying
y = 7
Solution
y = {-7.5, 7}