3(2y-6)=2(1-4y-1/2y)

Solution for 3(2y-6)=2(1-4y-1/2y) equation:

3(2y-6)=2(1-4y-1/2y)

We move all terms to the left:

3(2y-6)-(2(1-4y-1/2y))=0


Domain of the equation: 2y))!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

3(2y-6)-(2(-4y-1/2y+1))=0

We multiply parentheses

6y-(2(-4y-1/2y+1))-18=0

We multiply all the terms by the denominator


6y*2y-4y-18*2y-1+1))-(2(+1))=0

We add all the numbers together, and all the variables

6y*2y-4y-18*2y-1+1))-(21)=0

We add all the numbers together, and all the variables

-4y+6y*2y-18*2y=0

Wy multiply elements

12y^2-4y-36y=0

We add all the numbers together, and all the variables

12y^2-40y=0

a = 12; b = -40; c = 0;
Δ = b2-4ac
Δ = -402-4·12·0
Δ = 1600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1600}=40$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-40}{2*12}=\frac{0}{24}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+40}{2*12}=\frac{80}{24}
=3+1/3
$