A(x)=(x-2)(x+3)+(x-2)(2x-1)

Solution for A(x)=(x-2)(x+3)+(x-2)(2x-1) equation:

(A)=(A-2)(A+3)+(A-2)(2A-1)

We move all terms to the left:

(A)-((A-2)(A+3)+(A-2)(2A-1))=0

We multiply parentheses ..

-((+A^2+3A-2A-6)+(A-2)(2A-1))+A=0


We calculate terms in parentheses: -((+A^2+3A-2A-6)+(A-2)(2A-1)), so:

(+A^2+3A-2A-6)+(A-2)(2A-1)

We get rid of parentheses

A^2+3A-2A+(A-2)(2A-1)-6

We multiply parentheses ..

A^2+(+2A^2-1A-4A+2)+3A-2A-6

We add all the numbers together, and all the variables

A^2+(+2A^2-1A-4A+2)+A-6

We get rid of parentheses

A^2+2A^2-1A-4A+A+2-6

We add all the numbers together, and all the variables

3A^2-4A-4

Back to the equation:

-(3A^2-4A-4)


We add all the numbers together, and all the variables

A-(3A^2-4A-4)=0

We get rid of parentheses

-3A^2+A+4A+4=0

We add all the numbers together, and all the variables

-3A^2+5A+4=0

a = -3; b = 5; c = +4;
Δ = b2-4ac
Δ = 52-4·(-3)·4
Δ = 73
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-\sqrt{73}}{2*-3}=\frac{-5-\sqrt{73}}{-6}
$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{73}}{2*-3}=\frac{-5+\sqrt{73}}{-6}
$