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

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

Simplifying
7y + -1 = 2y(y + 3) + -2

Reorder the terms:
-1 + 7y = 2y(y + 3) + -2

Reorder the terms:
-1 + 7y = 2y(3 + y) + -2
-1 + 7y = (3 * 2y + y * 2y) + -2
-1 + 7y = (6y + 2y2) + -2

Reorder the terms:
-1 + 7y = -2 + 6y + 2y2

Solving
-1 + 7y = -2 + 6y + 2y2

Solving for variable 'y'.

Reorder the terms:
-1 + 2 + 7y + -6y + -2y2 = -2 + 6y + 2y2 + 2 + -6y + -2y2

Combine like terms: -1 + 2 = 1
1 + 7y + -6y + -2y2 = -2 + 6y + 2y2 + 2 + -6y + -2y2

Combine like terms: 7y + -6y = 1y
1 + 1y + -2y2 = -2 + 6y + 2y2 + 2 + -6y + -2y2

Reorder the terms:
1 + 1y + -2y2 = -2 + 2 + 6y + -6y + 2y2 + -2y2

Combine like terms: -2 + 2 = 0
1 + 1y + -2y2 = 0 + 6y + -6y + 2y2 + -2y2
1 + 1y + -2y2 = 6y + -6y + 2y2 + -2y2

Combine like terms: 6y + -6y = 0
1 + 1y + -2y2 = 0 + 2y2 + -2y2
1 + 1y + -2y2 = 2y2 + -2y2

Combine like terms: 2y2 + -2y2 = 0
1 + 1y + -2y2 = 0

Factor a trinomial.
(1 + -1y)(1 + 2y) = 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 '(1 + 2y)' equal to zero and attempt to solve:

Simplifying
1 + 2y = 0

Solving
1 + 2y = 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 + 2y = 0 + -1

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

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

Divide each side by '2'.
y = -0.5

Simplifying
y = -0.5
Solution
y = {1, -0.5}