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

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

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

We move all terms to the left:

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

We multiply parentheses ..

-((+12X^2+12X-6X-6))+X=0


We calculate terms in parentheses: -((+12X^2+12X-6X-6)), so:

(+12X^2+12X-6X-6)

We get rid of parentheses

12X^2+12X-6X-6

We add all the numbers together, and all the variables

12X^2+6X-6

Back to the equation:

-(12X^2+6X-6)


We add all the numbers together, and all the variables

X-(12X^2+6X-6)=0

We get rid of parentheses

-12X^2+X-6X+6=0

We add all the numbers together, and all the variables

-12X^2-5X+6=0

a = -12; b = -5; c = +6;
Δ = b2-4ac
Δ = -52-4·(-12)·6
Δ = 313
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-\sqrt{313}}{2*-12}=\frac{5-\sqrt{313}}{-24}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{313}}{2*-12}=\frac{5+\sqrt{313}}{-24}
$