(12-3x)(7x+5)=0

Solution for (12-3x)(7x+5)=0 equation:

(12-3x)(7x+5)=0

We add all the numbers together, and all the variables

(-3x+12)(7x+5)=0

We multiply parentheses ..

(-21x^2-15x+84x+60)=0

We get rid of parentheses

-21x^2-15x+84x+60=0

We add all the numbers together, and all the variables

-21x^2+69x+60=0

a = -21; b = 69; c = +60;
Δ = b2-4ac
Δ = 692-4·(-21)·60
Δ = 9801
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9801}=99$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(69)-99}{2*-21}=\frac{-168}{-42}
=+4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(69)+99}{2*-21}=\frac{30}{-42}
=-5/7
$