(Y-5)(3y-7)=3y^2+2y-13

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Solution for (Y-5)(3y-7)=3y^2+2y-13 equation: 


Simplifying
(Y + -5)(3y + -7) = 3y2 + 2y + -13

Reorder the terms:
(-5 + Y)(3y + -7) = 3y2 + 2y + -13

Reorder the terms:
(-5 + Y)(-7 + 3y) = 3y2 + 2y + -13

Multiply (-5 + Y) * (-7 + 3y)
(-5(-7 + 3y) + Y(-7 + 3y)) = 3y2 + 2y + -13
((-7 * -5 + 3y * -5) + Y(-7 + 3y)) = 3y2 + 2y + -13
((35 + -15y) + Y(-7 + 3y)) = 3y2 + 2y + -13
(35 + -15y + (-7 * Y + 3y * Y)) = 3y2 + 2y + -13
(35 + -15y + (-7Y + 3yY)) = 3y2 + 2y + -13

Reorder the terms:
(35 + -7Y + -15y + 3yY) = 3y2 + 2y + -13
(35 + -7Y + -15y + 3yY) = 3y2 + 2y + -13

Reorder the terms:
35 + -7Y + -15y + 3yY = -13 + 2y + 3y2

Solving
35 + -7Y + -15y + 3yY = -13 + 2y + 3y2

Solving for variable 'Y'.

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

Add '-35' to each side of the equation.
35 + -7Y + -15y + -35 + 3yY = -13 + 2y + -35 + 3y2

Reorder the terms:
35 + -35 + -7Y + -15y + 3yY = -13 + 2y + -35 + 3y2

Combine like terms: 35 + -35 = 0
0 + -7Y + -15y + 3yY = -13 + 2y + -35 + 3y2
-7Y + -15y + 3yY = -13 + 2y + -35 + 3y2

Reorder the terms:
-7Y + -15y + 3yY = -13 + -35 + 2y + 3y2

Combine like terms: -13 + -35 = -48
-7Y + -15y + 3yY = -48 + 2y + 3y2

Add '15y' to each side of the equation.
-7Y + -15y + 15y + 3yY = -48 + 2y + 15y + 3y2

Combine like terms: -15y + 15y = 0
-7Y + 0 + 3yY = -48 + 2y + 15y + 3y2
-7Y + 3yY = -48 + 2y + 15y + 3y2

Combine like terms: 2y + 15y = 17y
-7Y + 3yY = -48 + 17y + 3y2

Reorder the terms:
48 + -7Y + -17y + 3yY + -3y2 = -48 + 17y + 3y2 + 48 + -17y + -3y2

Reorder the terms:
48 + -7Y + -17y + 3yY + -3y2 = -48 + 48 + 17y + -17y + 3y2 + -3y2

Combine like terms: -48 + 48 = 0
48 + -7Y + -17y + 3yY + -3y2 = 0 + 17y + -17y + 3y2 + -3y2
48 + -7Y + -17y + 3yY + -3y2 = 17y + -17y + 3y2 + -3y2

Combine like terms: 17y + -17y = 0
48 + -7Y + -17y + 3yY + -3y2 = 0 + 3y2 + -3y2
48 + -7Y + -17y + 3yY + -3y2 = 3y2 + -3y2

Combine like terms: 3y2 + -3y2 = 0
48 + -7Y + -17y + 3yY + -3y2 = 0

The solution to this equation could not be determined.

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