6y+12=y(y+10)

Solution for 6y+12=y(y+10) equation:

Simplifying
6y + 12 = y(y + 10)

Reorder the terms:
12 + 6y = y(y + 10)

Reorder the terms:
12 + 6y = y(10 + y)
12 + 6y = (10 * y + y * y)
12 + 6y = (10y + y2)

Solving
12 + 6y = 10y + y2

Solving for variable 'y'.

Combine like terms: 6y + -10y = -4y
12 + -4y + -1y2 = 10y + y2 + -10y + -1y2

Reorder the terms:
12 + -4y + -1y2 = 10y + -10y + y2 + -1y2

Combine like terms: 10y + -10y = 0
12 + -4y + -1y2 = 0 + y2 + -1y2
12 + -4y + -1y2 = y2 + -1y2

Combine like terms: y2 + -1y2 = 0
12 + -4y + -1y2 = 0

Factor a trinomial.
(2 + -1y)(6 + y) = 0

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

Simplifying
2 + -1y = 0

Solving
2 + -1y = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1y = 0 + -2

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

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

Divide each side by '-1'.
y = 2

Simplifying
y = 2
Subproblem 2
Set the factor '(6 + y)' equal to zero and attempt to solve:

Simplifying
6 + y = 0

Solving
6 + y = 0

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

Add '-6' to each side of the equation.
6 + -6 + y = 0 + -6

Combine like terms: 6 + -6 = 0
0 + y = 0 + -6
y = 0 + -6

Combine like terms: 0 + -6 = -6
y = -6

Simplifying
y = -6
Solution
y = {2, -6}