12(y+1)+12y=7y(y+1)

Solution for 12(y+1)+12y=7y(y+1) equation:

Simplifying
12(y + 1) + 12y = 7y(y + 1)

Reorder the terms:
12(1 + y) + 12y = 7y(y + 1)
(1 * 12 + y * 12) + 12y = 7y(y + 1)
(12 + 12y) + 12y = 7y(y + 1)

Combine like terms: 12y + 12y = 24y
12 + 24y = 7y(y + 1)

Reorder the terms:
12 + 24y = 7y(1 + y)
12 + 24y = (1 * 7y + y * 7y)
12 + 24y = (7y + 7y2)

Solving
12 + 24y = 7y + 7y2

Solving for variable 'y'.

Combine like terms: 24y + -7y = 17y
12 + 17y + -7y2 = 7y + 7y2 + -7y + -7y2

Reorder the terms:
12 + 17y + -7y2 = 7y + -7y + 7y2 + -7y2

Combine like terms: 7y + -7y = 0
12 + 17y + -7y2 = 0 + 7y2 + -7y2
12 + 17y + -7y2 = 7y2 + -7y2

Combine like terms: 7y2 + -7y2 = 0
12 + 17y + -7y2 = 0

Factor a trinomial.
(3 + -1y)(4 + 7y) = 0

Subproblem 1
Set the factor '(3 + -1y)' equal to zero and attempt to solve:

Simplifying
3 + -1y = 0

Solving
3 + -1y = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1y = 0 + -3

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

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

Divide each side by '-1'.
y = 3

Simplifying
y = 3
Subproblem 2
Set the factor '(4 + 7y)' equal to zero and attempt to solve:

Simplifying
4 + 7y = 0

Solving
4 + 7y = 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 + 7y = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 7y = 0 + -4
7y = 0 + -4

Combine like terms: 0 + -4 = -4
7y = -4

Divide each side by '7'.
y = -0.5714285714

Simplifying
y = -0.5714285714
Solution
y = {3, -0.5714285714}