x=(2x+6)(3x-15)=0

Solution for x=(2x+6)(3x-15)=0 equation:

x=(2x+6)(3x-15)=0

We move all terms to the left:

x-((2x+6)(3x-15))=0

We multiply parentheses ..

-((+6x^2-30x+18x-90))+x=0


We calculate terms in parentheses: -((+6x^2-30x+18x-90)), so:

(+6x^2-30x+18x-90)

We get rid of parentheses

6x^2-30x+18x-90

We add all the numbers together, and all the variables

6x^2-12x-90

Back to the equation:

-(6x^2-12x-90)


We add all the numbers together, and all the variables

x-(6x^2-12x-90)=0

We get rid of parentheses

-6x^2+x+12x+90=0

We add all the numbers together, and all the variables

-6x^2+13x+90=0

a = -6; b = 13; c = +90;
Δ = b2-4ac
Δ = 132-4·(-6)·90
Δ = 2329
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{-(13)-\sqrt{2329}}{2*-6}=\frac{-13-\sqrt{2329}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+\sqrt{2329}}{2*-6}=\frac{-13+\sqrt{2329}}{-12}
$