3(y-1)=y^2-7

Solution for 3(y-1)=y^2-7 equation:

Simplifying
3(y + -1) = y2 + -7

Reorder the terms:
3(-1 + y) = y2 + -7
(-1 * 3 + y * 3) = y2 + -7
(-3 + 3y) = y2 + -7

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

Solving
-3 + 3y = -7 + y2

Solving for variable 'y'.

Reorder the terms:
-3 + 7 + 3y + -1y2 = -7 + y2 + 7 + -1y2

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

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

Combine like terms: -7 + 7 = 0
4 + 3y + -1y2 = 0 + y2 + -1y2
4 + 3y + -1y2 = y2 + -1y2

Combine like terms: y2 + -1y2 = 0
4 + 3y + -1y2 = 0

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

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

Simplifying
1 + y = 0

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

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

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

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