4(x+2)(2x-3)=-24

Solution for 4(x+2)(2x-3)=-24 equation:

4(x+2)(2x-3)=-24

We move all terms to the left:

4(x+2)(2x-3)-(-24)=0

We add all the numbers together, and all the variables

4(x+2)(2x-3)+24=0

We multiply parentheses ..

4(+2x^2-3x+4x-6)+24=0

We multiply parentheses

8x^2-12x+16x-24+24=0

We add all the numbers together, and all the variables

8x^2+4x=0

a = 8; b = 4; c = 0;
Δ = b2-4ac
Δ = 42-4·8·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4}{2*8}=\frac{-8}{16}
=-1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4}{2*8}=\frac{0}{16}
=0
$