(3x+12)(2+3x)=0

Solution for (3x+12)(2+3x)=0 equation:

(3x+12)(2+3x)=0

We add all the numbers together, and all the variables

(3x+12)(3x+2)=0

We multiply parentheses ..

(+9x^2+6x+36x+24)=0

We get rid of parentheses

9x^2+6x+36x+24=0

We add all the numbers together, and all the variables

9x^2+42x+24=0

a = 9; b = 42; c = +24;
Δ = b2-4ac
Δ = 422-4·9·24
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-30}{2*9}=\frac{-72}{18}
=-4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+30}{2*9}=\frac{-12}{18}
=-2/3
$