(2b+4)(4b+6)=-4b

Solution for (2b+4)(4b+6)=-4b equation:

(2b+4)(4b+6)=-4b

We move all terms to the left:

(2b+4)(4b+6)-(-4b)=0

We get rid of parentheses

(2b+4)(4b+6)+4b=0

We multiply parentheses ..

(+8b^2+12b+16b+24)+4b=0

We get rid of parentheses

8b^2+12b+16b+4b+24=0

We add all the numbers together, and all the variables

8b^2+32b+24=0

a = 8; b = 32; c = +24;
Δ = b2-4ac
Δ = 322-4·8·24
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-16}{2*8}=\frac{-48}{16}
=-3
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+16}{2*8}=\frac{-16}{16}
=-1
$