3(x+4)(x+7)=(3x+12)(3x+21)

Solution for 3(x+4)(x+7)=(3x+12)(3x+21) equation:

3(x+4)(x+7)=(3x+12)(3x+21)

We move all terms to the left:

3(x+4)(x+7)-((3x+12)(3x+21))=0

We multiply parentheses ..

3(+x^2+7x+4x+28)-((3x+12)(3x+21))=0


We calculate terms in parentheses: -((3x+12)(3x+21)), so:

(3x+12)(3x+21)

We multiply parentheses ..

(+9x^2+63x+36x+252)

We get rid of parentheses

9x^2+63x+36x+252

We add all the numbers together, and all the variables

9x^2+99x+252

Back to the equation:

-(9x^2+99x+252)


We multiply parentheses

3x^2+21x+12x-(9x^2+99x+252)+84=0

We get rid of parentheses

3x^2-9x^2+21x+12x-99x-252+84=0

We add all the numbers together, and all the variables

-6x^2-66x-168=0

a = -6; b = -66; c = -168;
Δ = b2-4ac
Δ = -662-4·(-6)·(-168)
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-66)-18}{2*-6}=\frac{48}{-12}
=-4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-66)+18}{2*-6}=\frac{84}{-12}
=-7
$