3r(r+3)=30

Divide each term in 3r(r+3)=30 by 3.

3r(r+3)3=303

Simplify 3r(r+3)3.

Cancel the common factor of 3.

Cancel the common factor.

3r(r+3)3=303

Divide r(r+3) by 1.

r(r+3)=303

r(r+3)=303

Apply the distributive property.

r⋅r+r⋅3=303

Simplify the expression.

Multiply r by r.

r2+r⋅3=303

Move 3 to the left of r.

r2+3r=303

r2+3r=303

r2+3r=303

Divide 30 by 3.

r2+3r=10

r2+3r=10

Move 10 to the left side of the equation by subtracting it from both sides.

r2+3r-10=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 -10 and whose sum is 3.

-2,5

Write the factored form using these integers.

(r-2)(r+5)=0

(r-2)(r+5)=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-2=0

r+5=0

Set the first factor equal to 0.

r-2=0

Add 2 to both sides of the equation.

r=2

r=2

Set the next factor equal to 0.

r+5=0

Subtract 5 from both sides of the equation.

r=-5

r=-5

The final solution is all the values that make (r-2)(r+5)=0 true.

r=2,-5

Solve for r 3r(r+3)=30