2(2+3x)(5+2x)=0

Solution for 2(2+3x)(5+2x)=0 equation:

2(2+3x)(5+2x)=0

We add all the numbers together, and all the variables

2(3x+2)(2x+5)=0

We multiply parentheses ..

2(+6x^2+15x+4x+10)=0

We multiply parentheses

12x^2+30x+8x+20=0

We add all the numbers together, and all the variables

12x^2+38x+20=0

a = 12; b = 38; c = +20;
Δ = b2-4ac
Δ = 382-4·12·20
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(38)-22}{2*12}=\frac{-60}{24}
=-2+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(38)+22}{2*12}=\frac{-16}{24}
=-2/3
$