(7+12)(y-3)-y(y+5)=24

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Solution for (7+12)(y-3)-y(y+5)=24 equation: 


Simplifying
(7 + 12)(y + -3) + -1y(y + 5) = 24

Combine like terms: 7 + 12 = 19
(19)(y + -3) + -1y(y + 5) = 24

Reorder the terms:
19(-3 + y) + -1y(y + 5) = 24
(-3 * 19 + y * 19) + -1y(y + 5) = 24
(-57 + 19y) + -1y(y + 5) = 24

Reorder the terms:
-57 + 19y + -1y(5 + y) = 24
-57 + 19y + (5 * -1y + y * -1y) = 24
-57 + 19y + (-5y + -1y2) = 24

Combine like terms: 19y + -5y = 14y
-57 + 14y + -1y2 = 24

Solving
-57 + 14y + -1y2 = 24

Solving for variable 'y'.

Reorder the terms:
-57 + -24 + 14y + -1y2 = 24 + -24

Combine like terms: -57 + -24 = -81
-81 + 14y + -1y2 = 24 + -24

Combine like terms: 24 + -24 = 0
-81 + 14y + -1y2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
81 + -14y + y2 = 0

Move the constant term to the right:

Add '-81' to each side of the equation.
81 + -14y + -81 + y2 = 0 + -81

Reorder the terms:
81 + -81 + -14y + y2 = 0 + -81

Combine like terms: 81 + -81 = 0
0 + -14y + y2 = 0 + -81
-14y + y2 = 0 + -81

Combine like terms: 0 + -81 = -81
-14y + y2 = -81

The y term is -14y.  Take half its coefficient (-7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
-14y + 49 + y2 = -81 + 49

Reorder the terms:
49 + -14y + y2 = -81 + 49

Combine like terms: -81 + 49 = -32
49 + -14y + y2 = -32

Factor a perfect square on the left side:
(y + -7)(y + -7) = -32

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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