(y-3)(2y+4)+8=(y+3)(y-2)

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Solution for (y-3)(2y+4)+8=(y+3)(y-2) equation: 


Simplifying
(y + -3)(2y + 4) + 8 = (y + 3)(y + -2)

Reorder the terms:
(-3 + y)(2y + 4) + 8 = (y + 3)(y + -2)

Reorder the terms:
(-3 + y)(4 + 2y) + 8 = (y + 3)(y + -2)

Multiply (-3 + y) * (4 + 2y)
(-3(4 + 2y) + y(4 + 2y)) + 8 = (y + 3)(y + -2)
((4 * -3 + 2y * -3) + y(4 + 2y)) + 8 = (y + 3)(y + -2)
((-12 + -6y) + y(4 + 2y)) + 8 = (y + 3)(y + -2)
(-12 + -6y + (4 * y + 2y * y)) + 8 = (y + 3)(y + -2)
(-12 + -6y + (4y + 2y2)) + 8 = (y + 3)(y + -2)

Combine like terms: -6y + 4y = -2y
(-12 + -2y + 2y2) + 8 = (y + 3)(y + -2)

Reorder the terms:
-12 + 8 + -2y + 2y2 = (y + 3)(y + -2)

Combine like terms: -12 + 8 = -4
-4 + -2y + 2y2 = (y + 3)(y + -2)

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

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

Multiply (3 + y) * (-2 + y)
-4 + -2y + 2y2 = (3(-2 + y) + y(-2 + y))
-4 + -2y + 2y2 = ((-2 * 3 + y * 3) + y(-2 + y))
-4 + -2y + 2y2 = ((-6 + 3y) + y(-2 + y))
-4 + -2y + 2y2 = (-6 + 3y + (-2 * y + y * y))
-4 + -2y + 2y2 = (-6 + 3y + (-2y + y2))

Combine like terms: 3y + -2y = 1y
-4 + -2y + 2y2 = (-6 + 1y + y2)

Solving
-4 + -2y + 2y2 = -6 + 1y + y2

Solving for variable 'y'.

Reorder the terms:
-4 + 6 + -2y + -1y + 2y2 + -1y2 = -6 + 1y + y2 + 6 + -1y + -1y2

Combine like terms: -4 + 6 = 2
2 + -2y + -1y + 2y2 + -1y2 = -6 + 1y + y2 + 6 + -1y + -1y2

Combine like terms: -2y + -1y = -3y
2 + -3y + 2y2 + -1y2 = -6 + 1y + y2 + 6 + -1y + -1y2

Combine like terms: 2y2 + -1y2 = 1y2
2 + -3y + 1y2 = -6 + 1y + y2 + 6 + -1y + -1y2

Reorder the terms:
2 + -3y + 1y2 = -6 + 6 + 1y + -1y + y2 + -1y2

Combine like terms: -6 + 6 = 0
2 + -3y + 1y2 = 0 + 1y + -1y + y2 + -1y2
2 + -3y + 1y2 = 1y + -1y + y2 + -1y2

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

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

Factor a trinomial.
(1 + -1y)(2 + -1y) = 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 '(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 = {1, 2}

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