(3d+12)(-21+9d)=0

Solution for (3d+12)(-21+9d)=0 equation:

(3d+12)(-21+9d)=0

We add all the numbers together, and all the variables

(3d+12)(9d-21)=0

We multiply parentheses ..

(+27d^2-63d+108d-252)=0

We get rid of parentheses

27d^2-63d+108d-252=0

We add all the numbers together, and all the variables

27d^2+45d-252=0

a = 27; b = 45; c = -252;
Δ = b2-4ac
Δ = 452-4·27·(-252)
Δ = 29241
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{29241}=171$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(45)-171}{2*27}=\frac{-216}{54}
=-4
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+171}{2*27}=\frac{126}{54}
=2+1/3
$