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

Solution for (3-2x)(4+3x)=0 equation:

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

(-6x^2-8x+9x+12)=0

We get rid of parentheses

-6x^2-8x+9x+12=0

We add all the numbers together, and all the variables

-6x^2+x+12=0

a = -6; b = 1; c = +12;
Δ = b2-4ac
Δ = 12-4·(-6)·12
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-17}{2*-6}=\frac{-18}{-12}
=1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+17}{2*-6}=\frac{16}{-12}
=-1+1/3
$