12x+3=3(4x+1)12x+3=3(4x+12

Solution for 12x+3=3(4x+1)12x+3=3(4x+12 equation:

12x+3=3(4x+1)12x+3=3(4x+12

We move all terms to the left:

12x+3-(3(4x+1)12x+3)=0


We calculate terms in parentheses: -(3(4x+1)12x+3), so:

3(4x+1)12x+3

We multiply parentheses

144x^2+36x+3

Back to the equation:

-(144x^2+36x+3)


We get rid of parentheses

-144x^2+12x-36x-3+3=0

We add all the numbers together, and all the variables

-144x^2-24x=0

a = -144; b = -24; c = 0;
Δ = b2-4ac
Δ = -242-4·(-144)·0
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-24}{2*-144}=\frac{0}{-288}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+24}{2*-144}=\frac{48}{-288}
=-1/6
$