-3b(2b+6)+5=-5b-13-b

Solution for -3b(2b+6)+5=-5b-13-b equation:

-3b(2b+6)+5=-5b-13-b

We move all terms to the left:

-3b(2b+6)+5-(-5b-13-b)=0

We add all the numbers together, and all the variables

-3b(2b+6)-(-6b-13)+5=0

We multiply parentheses

-6b^2-18b-(-6b-13)+5=0

We get rid of parentheses

-6b^2-18b+6b+13+5=0

We add all the numbers together, and all the variables

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

a = -6; b = -12; c = +18;
Δ = b2-4ac
Δ = -122-4·(-6)·18
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-24}{2*-6}=\frac{-12}{-12}
=1
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+24}{2*-6}=\frac{36}{-12}
=-3
$