1r(r+1)=r+(r+1)+5

Multiply r by 1.

r(r+1)=r+r+1+5

Apply the distributive property.

r⋅r+r⋅1=r+r+1+5

Simplify the expression.

Multiply r by r.

r2+r⋅1=r+r+1+5

Multiply r by 1.

r2+r=r+r+1+5

r2+r=r+r+1+5

r2+r=r+r+1+5

Add r and r.

r2+r=2r+1+5

Add 1 and 5.

r2+r=2r+6

r2+r=2r+6

Subtract 2r from both sides of the equation.

r2+r-2r=6

Subtract 2r from r.

r2-r=6

r2-r=6

Move 6 to the left side of the equation by subtracting it from both sides.

r2-r-6=0

Consider the form x2+bx+c. Find a pair of integers whose product is c and whose sum is b. In this case, whose product is -6 and whose sum is -1.

-3,2

Write the factored form using these integers.

(r-3)(r+2)=0

(r-3)(r+2)=0

If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.

r-3=0

r+2=0

Set the first factor equal to 0.

r-3=0

Add 3 to both sides of the equation.

r=3

r=3

Set the next factor equal to 0.

r+2=0

Subtract 2 from both sides of the equation.

r=-2

r=-2

The final solution is all the values that make (r-3)(r+2)=0 true.

r=3,-2

Solve for r 1r(r+1)=r+(r+1)+5