6y+y^2-3+y^2-4y+7-5y^2+8y-6=1

Solution for 6y+y^2-3+y^2-4y+7-5y^2+8y-6=1 equation:

Simplifying
6y + y2 + -3 + y2 + -4y + 7 + -5y2 + 8y + -6 = 1

Reorder the terms:
-3 + 7 + -6 + 6y + -4y + 8y + y2 + y2 + -5y2 = 1

Combine like terms: -3 + 7 = 4
4 + -6 + 6y + -4y + 8y + y2 + y2 + -5y2 = 1

Combine like terms: 4 + -6 = -2
-2 + 6y + -4y + 8y + y2 + y2 + -5y2 = 1

Combine like terms: 6y + -4y = 2y
-2 + 2y + 8y + y2 + y2 + -5y2 = 1

Combine like terms: 2y + 8y = 10y
-2 + 10y + y2 + y2 + -5y2 = 1

Combine like terms: y2 + y2 = 2y2
-2 + 10y + 2y2 + -5y2 = 1

Combine like terms: 2y2 + -5y2 = -3y2
-2 + 10y + -3y2 = 1

Solving
-2 + 10y + -3y2 = 1

Solving for variable 'y'.

Reorder the terms:
-2 + -1 + 10y + -3y2 = 1 + -1

Combine like terms: -2 + -1 = -3
-3 + 10y + -3y2 = 1 + -1

Combine like terms: 1 + -1 = 0
-3 + 10y + -3y2 = 0

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

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

Simplifying
-3 + y = 0

Solving
-3 + y = 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 + y = 0 + 3

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

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

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

Simplifying
1 + -3y = 0

Solving
1 + -3y = 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 + -3y = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3y = 0 + -1
-3y = 0 + -1

Combine like terms: 0 + -1 = -1
-3y = -1

Divide each side by '-3'.
y = 0.3333333333

Simplifying
y = 0.3333333333
Solution
y = {3, 0.3333333333}