3y^2-(y-5)(y-3)=2y^2+1

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Solution for 3y^2-(y-5)(y-3)=2y^2+1 equation: 


Simplifying
3y2 + -1(y + -5)(y + -3) = 2y2 + 1

Reorder the terms:
3y2 + -1(-5 + y)(y + -3) = 2y2 + 1

Reorder the terms:
3y2 + -1(-5 + y)(-3 + y) = 2y2 + 1

Multiply (-5 + y) * (-3 + y)
3y2 + -1(-5(-3 + y) + y(-3 + y)) = 2y2 + 1
3y2 + -1((-3 * -5 + y * -5) + y(-3 + y)) = 2y2 + 1
3y2 + -1((15 + -5y) + y(-3 + y)) = 2y2 + 1
3y2 + -1(15 + -5y + (-3 * y + y * y)) = 2y2 + 1
3y2 + -1(15 + -5y + (-3y + y2)) = 2y2 + 1

Combine like terms: -5y + -3y = -8y
3y2 + -1(15 + -8y + y2) = 2y2 + 1
3y2 + (15 * -1 + -8y * -1 + y2 * -1) = 2y2 + 1
3y2 + (-15 + 8y + -1y2) = 2y2 + 1

Reorder the terms:
-15 + 8y + 3y2 + -1y2 = 2y2 + 1

Combine like terms: 3y2 + -1y2 = 2y2
-15 + 8y + 2y2 = 2y2 + 1

Reorder the terms:
-15 + 8y + 2y2 = 1 + 2y2

Add '-2y2' to each side of the equation.
-15 + 8y + 2y2 + -2y2 = 1 + 2y2 + -2y2

Combine like terms: 2y2 + -2y2 = 0
-15 + 8y + 0 = 1 + 2y2 + -2y2
-15 + 8y = 1 + 2y2 + -2y2

Combine like terms: 2y2 + -2y2 = 0
-15 + 8y = 1 + 0
-15 + 8y = 1

Solving
-15 + 8y = 1

Solving for variable 'y'.

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

Add '15' to each side of the equation.
-15 + 15 + 8y = 1 + 15

Combine like terms: -15 + 15 = 0
0 + 8y = 1 + 15
8y = 1 + 15

Combine like terms: 1 + 15 = 16
8y = 16

Divide each side by '8'.
y = 2

Simplifying
y = 2

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