y^2-7=3y-3

Solution for y^2-7=3y-3 equation:

Simplifying
y2 + -7 = 3y + -3

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

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

Solving
-7 + y2 = -3 + 3y

Solving for variable 'y'.

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

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

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

Combine like terms: -3 + 3 = 0
-4 + -3y + y2 = 0 + 3y + -3y
-4 + -3y + y2 = 3y + -3y

Combine like terms: 3y + -3y = 0
-4 + -3y + y2 = 0

Factor a trinomial.
(-1 + -1y)(4 + -1y) = 0

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 '(4 + -1y)' equal to zero and attempt to solve:

Simplifying
4 + -1y = 0

Solving
4 + -1y = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1y = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1y = 0 + -4
-1y = 0 + -4

Combine like terms: 0 + -4 = -4
-1y = -4

Divide each side by '-1'.
y = 4

Simplifying
y = 4
Solution
y = {-1, 4}