(4x+2)(2x-3)-(4x+2)(-5x+1)=0

Solution for (4x+2)(2x-3)-(4x+2)(-5x+1)=0 equation:

(4x+2)(2x-3)-(4x+2)(-5x+1)=0

We multiply parentheses ..

(+8x^2-12x+4x-6)-(4x+2)(-5x+1)=0

We get rid of parentheses

8x^2-12x+4x-(4x+2)(-5x+1)-6=0

We multiply parentheses ..

8x^2-(-20x^2+4x-10x+2)-12x+4x-6=0

We add all the numbers together, and all the variables

8x^2-(-20x^2+4x-10x+2)-8x-6=0

We get rid of parentheses

8x^2+20x^2-4x+10x-8x-2-6=0

We add all the numbers together, and all the variables

28x^2-2x-8=0

a = 28; b = -2; c = -8;
Δ = b2-4ac
Δ = -22-4·28·(-8)
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-30}{2*28}=\frac{-28}{56}
=-1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+30}{2*28}=\frac{32}{56}
=4/7
$