2y^2-7(y+3)=(y+5)(y-2)

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Solution for 2y^2-7(y+3)=(y+5)(y-2) equation: 


Simplifying
2y2 + -7(y + 3) = (y + 5)(y + -2)

Reorder the terms:
2y2 + -7(3 + y) = (y + 5)(y + -2)
2y2 + (3 * -7 + y * -7) = (y + 5)(y + -2)
2y2 + (-21 + -7y) = (y + 5)(y + -2)

Reorder the terms:
-21 + -7y + 2y2 = (y + 5)(y + -2)

Reorder the terms:
-21 + -7y + 2y2 = (5 + y)(y + -2)

Reorder the terms:
-21 + -7y + 2y2 = (5 + y)(-2 + y)

Multiply (5 + y) * (-2 + y)
-21 + -7y + 2y2 = (5(-2 + y) + y(-2 + y))
-21 + -7y + 2y2 = ((-2 * 5 + y * 5) + y(-2 + y))
-21 + -7y + 2y2 = ((-10 + 5y) + y(-2 + y))
-21 + -7y + 2y2 = (-10 + 5y + (-2 * y + y * y))
-21 + -7y + 2y2 = (-10 + 5y + (-2y + y2))

Combine like terms: 5y + -2y = 3y
-21 + -7y + 2y2 = (-10 + 3y + y2)

Solving
-21 + -7y + 2y2 = -10 + 3y + y2

Solving for variable 'y'.

Reorder the terms:
-21 + 10 + -7y + -3y + 2y2 + -1y2 = -10 + 3y + y2 + 10 + -3y + -1y2

Combine like terms: -21 + 10 = -11
-11 + -7y + -3y + 2y2 + -1y2 = -10 + 3y + y2 + 10 + -3y + -1y2

Combine like terms: -7y + -3y = -10y
-11 + -10y + 2y2 + -1y2 = -10 + 3y + y2 + 10 + -3y + -1y2

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

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

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

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

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

Factor a trinomial.
(-1 + -1y)(11 + -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 '(11 + -1y)' equal to zero and attempt to solve:

Simplifying
11 + -1y = 0

Solving
11 + -1y = 0

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

Add '-11' to each side of the equation.
11 + -11 + -1y = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -1y = 0 + -11
-1y = 0 + -11

Combine like terms: 0 + -11 = -11
-1y = -11

Divide each side by '-1'.
y = 11

Simplifying
y = 11
Solution
y = {-1, 11}

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