-2a(3a-6)=-6a-9+21

Solution for -2a(3a-6)=-6a-9+21 equation:

-2a(3a-6)=-6a-9+21

We move all terms to the left:

-2a(3a-6)-(-6a-9+21)=0

We add all the numbers together, and all the variables

-2a(3a-6)-(-6a+12)=0

We multiply parentheses

-6a^2+12a-(-6a+12)=0

We get rid of parentheses

-6a^2+12a+6a-12=0

We add all the numbers together, and all the variables

-6a^2+18a-12=0

a = -6; b = 18; c = -12;
Δ = b2-4ac
Δ = 182-4·(-6)·(-12)
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-6}{2*-6}=\frac{-24}{-12}
=+2
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+6}{2*-6}=\frac{-12}{-12}
=1
$