2(y^2-1)=3y

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

Simplifying
2(y2 + -1) = 3y

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

Solving
-2 + 2y2 = 3y

Solving for variable 'y'.

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

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

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

Subproblem 1
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
Subproblem 2
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
Solution
y = {-0.5, 2}