3(x-2)(x+2)-5(x+2)=(x+2)(3x-11)

Solution for 3(x-2)(x+2)-5(x+2)=(x+2)(3x-11) equation:

3(x-2)(x+2)-5(x+2)=(x+2)(3x-11)

We move all terms to the left:

3(x-2)(x+2)-5(x+2)-((x+2)(3x-11))=0

We use the square of the difference formula

x^2-5(x+2)-((x+2)(3x-11))-4=0

We multiply parentheses

x^2-5x-((x+2)(3x-11))-10-4=0

We multiply parentheses ..

x^2-((+3x^2-11x+6x-22))-5x-10-4=0


We calculate terms in parentheses: -((+3x^2-11x+6x-22)), so:

(+3x^2-11x+6x-22)

We get rid of parentheses

3x^2-11x+6x-22

We add all the numbers together, and all the variables

3x^2-5x-22

Back to the equation:

-(3x^2-5x-22)


We add all the numbers together, and all the variables

x^2-5x-(3x^2-5x-22)-14=0

We get rid of parentheses

x^2-3x^2-5x+5x+22-14=0

We add all the numbers together, and all the variables

-2x^2+8=0

a = -2; b = 0; c = +8;
Δ = b2-4ac
Δ = 02-4·(-2)·8
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8}{2*-2}=\frac{-8}{-4}
=+2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8}{2*-2}=\frac{8}{-4}
=-2
$