3y+3=7+2y-4+y*y

Solution for 3y+3=7+2y-4+y*y equation:

Simplifying
3y + 3 = 7 + 2y + -4 + y * y

Reorder the terms:
3 + 3y = 7 + 2y + -4 + y * y

Multiply y * y
3 + 3y = 7 + 2y + -4 + y2

Reorder the terms:
3 + 3y = 7 + -4 + 2y + y2

Combine like terms: 7 + -4 = 3
3 + 3y = 3 + 2y + y2

Add '-3' to each side of the equation.
3 + -3 + 3y = 3 + 2y + -3 + y2

Combine like terms: 3 + -3 = 0
0 + 3y = 3 + 2y + -3 + y2
3y = 3 + 2y + -3 + y2

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

Combine like terms: 3 + -3 = 0
3y = 0 + 2y + y2
3y = 2y + y2

Solving
3y = 2y + y2

Solving for variable 'y'.

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

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

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

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

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

Subproblem 1
Set the factor 'y' equal to zero and attempt to solve:

Simplifying
y = 0

Solving
y = 0

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

Simplifying
y = 0
Subproblem 2
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
Solution
y = {0, 1}