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

Solution for (4x+6)(3x-2)=0 equation:

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

We multiply parentheses ..

(+12x^2-8x+18x-12)=0

We get rid of parentheses

12x^2-8x+18x-12=0

We add all the numbers together, and all the variables

12x^2+10x-12=0

a = 12; b = 10; c = -12;
Δ = b2-4ac
Δ = 102-4·12·(-12)
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-26}{2*12}=\frac{-36}{24}
=-1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+26}{2*12}=\frac{16}{24}
=2/3
$