Question
Solve the equation
y1=−1,y2=6
Evaluate
y−y6=5
Find the domain
y−y6=5,y=0
Multiply both sides of the equation by LCD
(y−y6)y=5y
Simplify the equation
More Steps

Evaluate
(y−y6)y
Apply the distributive property
y×y−y6×y
Simplify
y×y−6
Multiply the terms
y2−6
y2−6=5y
Move the expression to the left side
y2−6−5y=0
Factor the expression
More Steps

Evaluate
y2−6−5y
Reorder the terms
y2−5y−6
Rewrite the expression
y2+(1−6)y−6
Calculate
y2+y−6y−6
Rewrite the expression
y×y+y−6y−6
Factor out y from the expression
y(y+1)−6y−6
Factor out −6 from the expression
y(y+1)−6(y+1)
Factor out y+1 from the expression
(y−6)(y+1)
(y−6)(y+1)=0
When the product of factors equals 0,at least one factor is 0
y−6=0y+1=0
Solve the equation for y
More Steps

Evaluate
y−6=0
Move the constant to the right-hand side and change its sign
y=0+6
Removing 0 doesn't change the value,so remove it from the expression
y=6
y=6y+1=0
Solve the equation for y
More Steps

Evaluate
y+1=0
Move the constant to the right-hand side and change its sign
y=0−1
Removing 0 doesn't change the value,so remove it from the expression
y=−1
y=6y=−1
Check if the solution is in the defined range
y=6y=−1,y=0
Find the intersection of the solution and the defined range
y=6y=−1
Solution
y1=−1,y2=6
Show Solution
