Verified answer

π(r+6) ² = 15(2πr) + 2 πr²

First, recognize that since everything on both sides of the equal is being multiplied by π, it can be factored out of the equation entirely.

π(r+6) ² = 15(2πr) + 2 πr²

π(r+6) ² = π[15(2r) + 2r²]

(r+6) ² = [15(2r) + 2r²]

>> multiply out the parenthetical expressions

(r² + 12r + 36) = 30r + 2r²

r² + 12r + 36 = 30r + 2r²

>> move everything to one side of the equal sign

0 = r² + 18r - 36

>> solve for r using the quadratic formula

r = (1/2)[-18 ± √(324+144)]

>> simplify using rules of algebra for radicals

r = (1/2)(-18) ± (1/2)√(468)

r = -9 ± (1/2)√468

r = -9 ± (1/2)√(36*13)

r = -9 ± (1/2)(6)√13

r = -9 ± 3√13

ANSWER

r = -9 + 3√13

r = -9 - 3√13

The π is just a distraction.

Those answers check out ok in Microsoft Excel

It looks like it's going to be a weird quadratic equation.

ugh.

Lose the π and work from there.