x+10=(x+12)(4x-6)

Solution for x+10=(x+12)(4x-6) equation:

x+10=(x+12)(4x-6)

We move all terms to the left:

x+10-((x+12)(4x-6))=0

We multiply parentheses ..

-((+4x^2-6x+48x-72))+x+10=0


We calculate terms in parentheses: -((+4x^2-6x+48x-72)), so:

(+4x^2-6x+48x-72)

We get rid of parentheses

4x^2-6x+48x-72

We add all the numbers together, and all the variables

4x^2+42x-72

Back to the equation:

-(4x^2+42x-72)


We add all the numbers together, and all the variables

x-(4x^2+42x-72)+10=0

We get rid of parentheses

-4x^2+x-42x+72+10=0

We add all the numbers together, and all the variables

-4x^2-41x+82=0

a = -4; b = -41; c = +82;
Δ = b2-4ac
Δ = -412-4·(-4)·82
Δ = 2993
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{-(-41)-\sqrt{2993}}{2*-4}=\frac{41-\sqrt{2993}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-41)+\sqrt{2993}}{2*-4}=\frac{41+\sqrt{2993}}{-8}
$