(2y+1)(y-3)-3y(y+2)=y(2-y)+10

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Solution for (2y+1)(y-3)-3y(y+2)=y(2-y)+10 equation: 


Simplifying
(2y + 1)(y + -3) + -3y(y + 2) = y(2 + -1y) + 10

Reorder the terms:
(1 + 2y)(y + -3) + -3y(y + 2) = y(2 + -1y) + 10

Reorder the terms:
(1 + 2y)(-3 + y) + -3y(y + 2) = y(2 + -1y) + 10

Multiply (1 + 2y) * (-3 + y)
(1(-3 + y) + 2y * (-3 + y)) + -3y(y + 2) = y(2 + -1y) + 10
((-3 * 1 + y * 1) + 2y * (-3 + y)) + -3y(y + 2) = y(2 + -1y) + 10
((-3 + 1y) + 2y * (-3 + y)) + -3y(y + 2) = y(2 + -1y) + 10
(-3 + 1y + (-3 * 2y + y * 2y)) + -3y(y + 2) = y(2 + -1y) + 10
(-3 + 1y + (-6y + 2y2)) + -3y(y + 2) = y(2 + -1y) + 10

Combine like terms: 1y + -6y = -5y
(-3 + -5y + 2y2) + -3y(y + 2) = y(2 + -1y) + 10

Reorder the terms:
-3 + -5y + 2y2 + -3y(2 + y) = y(2 + -1y) + 10
-3 + -5y + 2y2 + (2 * -3y + y * -3y) = y(2 + -1y) + 10
-3 + -5y + 2y2 + (-6y + -3y2) = y(2 + -1y) + 10

Reorder the terms:
-3 + -5y + -6y + 2y2 + -3y2 = y(2 + -1y) + 10

Combine like terms: -5y + -6y = -11y
-3 + -11y + 2y2 + -3y2 = y(2 + -1y) + 10

Combine like terms: 2y2 + -3y2 = -1y2
-3 + -11y + -1y2 = y(2 + -1y) + 10
-3 + -11y + -1y2 = (2 * y + -1y * y) + 10
-3 + -11y + -1y2 = (2y + -1y2) + 10

Reorder the terms:
-3 + -11y + -1y2 = 10 + 2y + -1y2

Add 'y2' to each side of the equation.
-3 + -11y + -1y2 + y2 = 10 + 2y + -1y2 + y2

Combine like terms: -1y2 + y2 = 0
-3 + -11y + 0 = 10 + 2y + -1y2 + y2
-3 + -11y = 10 + 2y + -1y2 + y2

Combine like terms: -1y2 + y2 = 0
-3 + -11y = 10 + 2y + 0
-3 + -11y = 10 + 2y

Solving
-3 + -11y = 10 + 2y

Solving for variable 'y'.

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

Add '-2y' to each side of the equation.
-3 + -11y + -2y = 10 + 2y + -2y

Combine like terms: -11y + -2y = -13y
-3 + -13y = 10 + 2y + -2y

Combine like terms: 2y + -2y = 0
-3 + -13y = 10 + 0
-3 + -13y = 10

Add '3' to each side of the equation.
-3 + 3 + -13y = 10 + 3

Combine like terms: -3 + 3 = 0
0 + -13y = 10 + 3
-13y = 10 + 3

Combine like terms: 10 + 3 = 13
-13y = 13

Divide each side by '-13'.
y = -1

Simplifying
y = -1

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