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

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


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

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

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

Multiply (5 + y) * (-2 + y)
(5(-2 + y) + y(-2 + y)) = 2 + 3y
((-2 * 5 + y * 5) + y(-2 + y)) = 2 + 3y
((-10 + 5y) + y(-2 + y)) = 2 + 3y
(-10 + 5y + (-2 * y + y * y)) = 2 + 3y
(-10 + 5y + (-2y + y2)) = 2 + 3y

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

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

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

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

Solving
-10 + y2 = 2

Solving for variable 'y'.

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

Add '10' to each side of the equation.
-10 + 10 + y2 = 2 + 10

Combine like terms: -10 + 10 = 0
0 + y2 = 2 + 10
y2 = 2 + 10

Combine like terms: 2 + 10 = 12
y2 = 12

Simplifying
y2 = 12

Take the square root of each side:
y = {-3.464101615, 3.464101615}

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