# Solve for r (r-3)(r+9)=12 (r-3)(r+9)=12
Simplify (r-3)(r+9).
Expand (r-3)(r+9) using the FOIL Method.
Apply the distributive property.
r(r+9)-3(r+9)=12
Apply the distributive property.
r⋅r+r⋅9-3(r+9)=12
Apply the distributive property.
r⋅r+r⋅9-3r-3⋅9=12
r⋅r+r⋅9-3r-3⋅9=12
Simplify and combine like terms.
Simplify each term.
Multiply r by r.
r2+r⋅9-3r-3⋅9=12
Move 9 to the left of r.
r2+9⋅r-3r-3⋅9=12
Multiply -3 by 9.
r2+9r-3r-27=12
r2+9r-3r-27=12
Subtract 3r from 9r.
r2+6r-27=12
r2+6r-27=12
r2+6r-27=12
Move all terms to the left side of the equation and simplify.
Move 12 to the left side of the equation by subtracting it from both sides.
r2+6r-27-12=0
Subtract 12 from -27.
r2+6r-39=0
r2+6r-39=0
Use the quadratic formula to find the solutions.
-b±b2-4(ac)2a
Substitute the values a=1, b=6, and c=-39 into the quadratic formula and solve for r.
-6±62-4⋅(1⋅-39)2⋅1
Simplify.
Simplify the numerator.
Raise 6 to the power of 2.
r=-6±36-4⋅(1⋅-39)2⋅1
Multiply -39 by 1.
r=-6±36-4⋅-392⋅1
Multiply -4 by -39.
r=-6±36+1562⋅1
Add 36 and 156.
r=-6±1922⋅1
Rewrite 192 as 82⋅3.
Factor 64 out of 192.
r=-6±64(3)2⋅1
Rewrite 64 as 82.
r=-6±82⋅32⋅1
r=-6±82⋅32⋅1
Pull terms out from under the radical.
r=-6±832⋅1
r=-6±832⋅1
Multiply 2 by 1.
r=-6±832
Simplify -6±832.
r=-3±43
r=-3±43
The final answer is the combination of both solutions.
r=-3+43,-3-43
The result can be shown in multiple forms.
Exact Form:
r=-3+43,-3-43
Decimal Form:
r=3.92820323…,-9.92820323…
Solve for r (r-3)(r+9)=12

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