7y+3y^2=6+10y

Solution for 7y+3y^2=6+10y equation:

Simplifying
7y + 3y2 = 6 + 10y

Solving
7y + 3y2 = 6 + 10y

Solving for variable 'y'.

Reorder the terms:
-6 + 7y + -10y + 3y2 = 6 + 10y + -6 + -10y

Combine like terms: 7y + -10y = -3y
-6 + -3y + 3y2 = 6 + 10y + -6 + -10y

Reorder the terms:
-6 + -3y + 3y2 = 6 + -6 + 10y + -10y

Combine like terms: 6 + -6 = 0
-6 + -3y + 3y2 = 0 + 10y + -10y
-6 + -3y + 3y2 = 10y + -10y

Combine like terms: 10y + -10y = 0
-6 + -3y + 3y2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-2 + -1y + y2) = 0

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

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

Simplifying
-1 + -1y = 0

Solving
-1 + -1y = 0

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

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

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

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

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

Simplifying
y = -1
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, 2}