4(x+15)+4x=x(x+15)

Solution for 4(x+15)+4x=x(x+15) equation:

4(x+15)+4x=x(x+15)

We move all terms to the left:

4(x+15)+4x-(x(x+15))=0

We add all the numbers together, and all the variables

4x+4(x+15)-(x(x+15))=0

We multiply parentheses

4x+4x-(x(x+15))+60=0


We calculate terms in parentheses: -(x(x+15)), so:

x(x+15)

We multiply parentheses

x^2+15x

Back to the equation:

-(x^2+15x)


We add all the numbers together, and all the variables

8x-(x^2+15x)+60=0

We get rid of parentheses

-x^2+8x-15x+60=0

We add all the numbers together, and all the variables

-1x^2-7x+60=0

a = -1; b = -7; c = +60;
Δ = b2-4ac
Δ = -72-4·(-1)·60
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-17}{2*-1}=\frac{-10}{-2}
=+5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+17}{2*-1}=\frac{24}{-2}
=-12
$