y^2+8=3y(y-2)

Solution for y^2+8=3y(y-2) equation:

Simplifying
y2 + 8 = 3y(y + -2)

Reorder the terms:
8 + y2 = 3y(y + -2)

Reorder the terms:
8 + y2 = 3y(-2 + y)
8 + y2 = (-2 * 3y + y * 3y)
8 + y2 = (-6y + 3y2)

Solving
8 + y2 = -6y + 3y2

Solving for variable 'y'.

Reorder the terms:
8 + 6y + y2 + -3y2 = -6y + 3y2 + 6y + -3y2

Combine like terms: y2 + -3y2 = -2y2
8 + 6y + -2y2 = -6y + 3y2 + 6y + -3y2

Reorder the terms:
8 + 6y + -2y2 = -6y + 6y + 3y2 + -3y2

Combine like terms: -6y + 6y = 0
8 + 6y + -2y2 = 0 + 3y2 + -3y2
8 + 6y + -2y2 = 3y2 + -3y2

Combine like terms: 3y2 + -3y2 = 0
8 + 6y + -2y2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(4 + 3y + -1y2) = 0

Factor a trinomial.
2((4 + -1y)(1 + y)) = 0

Ignore the factor 2.
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}