A=(-2x+5x-6)(1-x)

Solution for A=(-2x+5x-6)(1-x) equation:

=(-2A+5A-6)(1-A)

We move all terms to the left:

-((-2A+5A-6)(1-A))=0

We add all the numbers together, and all the variables

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

We multiply parentheses ..

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


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

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

We get rid of parentheses

-3A^2+3A+6A-6

We add all the numbers together, and all the variables

-3A^2+9A-6

Back to the equation:

-(-3A^2+9A-6)


We get rid of parentheses

3A^2-9A+6=0

a = 3; b = -9; c = +6;
Δ = b2-4ac
Δ = -92-4·3·6
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-3}{2*3}=\frac{6}{6}
=1
$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+3}{2*3}=\frac{12}{6}
=2
$