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

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


Simplifying
(y + 3)(y + -1) + -1y(y + -2) = 2y2 + -3

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

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

Multiply (3 + y) * (-1 + y)
(3(-1 + y) + y(-1 + y)) + -1y(y + -2) = 2y2 + -3
((-1 * 3 + y * 3) + y(-1 + y)) + -1y(y + -2) = 2y2 + -3
((-3 + 3y) + y(-1 + y)) + -1y(y + -2) = 2y2 + -3
(-3 + 3y + (-1 * y + y * y)) + -1y(y + -2) = 2y2 + -3
(-3 + 3y + (-1y + y2)) + -1y(y + -2) = 2y2 + -3

Combine like terms: 3y + -1y = 2y
(-3 + 2y + y2) + -1y(y + -2) = 2y2 + -3

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

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

Combine like terms: 2y + 2y = 4y
-3 + 4y + y2 + -1y2 = 2y2 + -3

Combine like terms: y2 + -1y2 = 0
-3 + 4y + 0 = 2y2 + -3
-3 + 4y = 2y2 + -3

Reorder the terms:
-3 + 4y = -3 + 2y2

Add '3' to each side of the equation.
-3 + 3 + 4y = -3 + 3 + 2y2

Combine like terms: -3 + 3 = 0
0 + 4y = -3 + 3 + 2y2
4y = -3 + 3 + 2y2

Combine like terms: -3 + 3 = 0
4y = 0 + 2y2
4y = 2y2

Solving
4y = 2y2

Solving for variable 'y'.

Combine like terms: 2y2 + -2y2 = 0
4y + -2y2 = 0

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

Ignore the factor 2.

Subproblem 1
Set the factor 'y' equal to zero and attempt to solve:

Simplifying
y = 0

Solving
y = 0

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

Simplifying
y = 0

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, 2}

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