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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

12x^2+6x-(-3(2x-3))=0


We calculate terms in parentheses: -(-3(2x-3)), so:

-3(2x-3)

We multiply parentheses

-6x+9

Back to the equation:

-(-6x+9)


We get rid of parentheses

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

We add all the numbers together, and all the variables

12x^2+12x-9=0

a = 12; b = 12; c = -9;
Δ = b2-4ac
Δ = 122-4·12·(-9)
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{-(12)-24}{2*12}=\frac{-36}{24}
=-1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+24}{2*12}=\frac{12}{24}
=1/2
$