x+10=(x+4)(x+6)

Solution for x+10=(x+4)(x+6) equation:

x+10=(x+4)(x+6)

We move all terms to the left:

x+10-((x+4)(x+6))=0

We multiply parentheses ..

-((+x^2+6x+4x+24))+x+10=0


We calculate terms in parentheses: -((+x^2+6x+4x+24)), so:

(+x^2+6x+4x+24)

We get rid of parentheses

x^2+6x+4x+24

We add all the numbers together, and all the variables

x^2+10x+24

Back to the equation:

-(x^2+10x+24)


We add all the numbers together, and all the variables

x-(x^2+10x+24)+10=0

We get rid of parentheses

-x^2+x-10x-24+10=0

We add all the numbers together, and all the variables

-1x^2-9x-14=0

a = -1; b = -9; c = -14;
Δ = b2-4ac
Δ = -92-4·(-1)·(-14)
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-5}{2*-1}=\frac{4}{-2}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+5}{2*-1}=\frac{14}{-2}
=-7
$