(4y+5)(y+6)=-3(4y+5)

Solution for (4y+5)(y+6)=-3(4y+5) equation:

(4y+5)(y+6)=-3(4y+5)

We move all terms to the left:

(4y+5)(y+6)-(-3(4y+5))=0

We multiply parentheses ..

(+4y^2+24y+5y+30)-(-3(4y+5))=0


We calculate terms in parentheses: -(-3(4y+5)), so:

-3(4y+5)

We multiply parentheses

-12y-15

Back to the equation:

-(-12y-15)


We get rid of parentheses

4y^2+24y+5y+12y+30+15=0

We add all the numbers together, and all the variables

4y^2+41y+45=0

a = 4; b = 41; c = +45;
Δ = b2-4ac
Δ = 412-4·4·45
Δ = 961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{961}=31$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(41)-31}{2*4}=\frac{-72}{8}
=-9
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(41)+31}{2*4}=\frac{-10}{8}
=-1+1/4
$