(-4x+4)(-9x+4)+(-4x+4)(6x+3)=0

Solution for (-4x+4)(-9x+4)+(-4x+4)(6x+3)=0 equation:

(-4x+4)(-9x+4)+(-4x+4)(6x+3)=0

We multiply parentheses ..

(+36x^2-16x-36x+16)+(-4x+4)(6x+3)=0

We get rid of parentheses

36x^2-16x-36x+(-4x+4)(6x+3)+16=0

We multiply parentheses ..

36x^2+(-24x^2-12x+24x+12)-16x-36x+16=0

We add all the numbers together, and all the variables

36x^2+(-24x^2-12x+24x+12)-52x+16=0

We get rid of parentheses

36x^2-24x^2-12x+24x-52x+12+16=0

We add all the numbers together, and all the variables

12x^2-40x+28=0

a = 12; b = -40; c = +28;
Δ = b2-4ac
Δ = -402-4·12·28
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-16}{2*12}=\frac{24}{24}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+16}{2*12}=\frac{56}{24}
=2+1/3
$