(y-5)(y+1)=y^2+13

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Solution for (y-5)(y+1)=y^2+13 equation: 


Simplifying
(y + -5)(y + 1) = y2 + 13

Reorder the terms:
(-5 + y)(y + 1) = y2 + 13

Reorder the terms:
(-5 + y)(1 + y) = y2 + 13

Multiply (-5 + y) * (1 + y)
(-5(1 + y) + y(1 + y)) = y2 + 13
((1 * -5 + y * -5) + y(1 + y)) = y2 + 13
((-5 + -5y) + y(1 + y)) = y2 + 13
(-5 + -5y + (1 * y + y * y)) = y2 + 13
(-5 + -5y + (1y + y2)) = y2 + 13

Combine like terms: -5y + 1y = -4y
(-5 + -4y + y2) = y2 + 13

Reorder the terms:
-5 + -4y + y2 = 13 + y2

Add '-1y2' to each side of the equation.
-5 + -4y + y2 + -1y2 = 13 + y2 + -1y2

Combine like terms: y2 + -1y2 = 0
-5 + -4y + 0 = 13 + y2 + -1y2
-5 + -4y = 13 + y2 + -1y2

Combine like terms: y2 + -1y2 = 0
-5 + -4y = 13 + 0
-5 + -4y = 13

Solving
-5 + -4y = 13

Solving for variable 'y'.

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

Add '5' to each side of the equation.
-5 + 5 + -4y = 13 + 5

Combine like terms: -5 + 5 = 0
0 + -4y = 13 + 5
-4y = 13 + 5

Combine like terms: 13 + 5 = 18
-4y = 18

Divide each side by '-4'.
y = -4.5

Simplifying
y = -4.5

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