-6(1-6r)=-2r(r+3)

Solution for -6(1-6r)=-2r(r+3) equation:

-6(1-6r)=-2r(r+3)

We move all terms to the left:

-6(1-6r)-(-2r(r+3))=0

We add all the numbers together, and all the variables

-6(-6r+1)-(-2r(r+3))=0

We multiply parentheses

36r-(-2r(r+3))-6=0


We calculate terms in parentheses: -(-2r(r+3)), so:

-2r(r+3)

We multiply parentheses

-2r^2-6r

Back to the equation:

-(-2r^2-6r)


We get rid of parentheses

2r^2+6r+36r-6=0

We add all the numbers together, and all the variables

2r^2+42r-6=0

a = 2; b = 42; c = -6;
Δ = b2-4ac
Δ = 422-4·2·(-6)
Δ = 1812
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1812}=\sqrt{4*453}=\sqrt{4}*\sqrt{453}=2\sqrt{453}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-2\sqrt{453}}{2*2}=\frac{-42-2\sqrt{453}}{4}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+2\sqrt{453}}{2*2}=\frac{-42+2\sqrt{453}}{4}
$