$a)$

$x^2-{\left(2-x\right)}^2=8$

$x^2-\left(4-4x+x^2\right)=8$

$x^2-4+4x-x^2=8$

$-4+4x=8\mid +4$

$4x=12\mid :4$

$x=3$

 

$b)$

${\left(3x+1\right)}^2-9x^2=7$

$9x^2+6x+1-9x^2=7$

$6x+1=7\mid -1$

$6x=6\mid :6$

$x=1$

 

 

$c)$

$\left(4-x\right)\left(4+x\right)=2x-x^2$

$16-x^2=2x-x^2\mid +x^2$

$16=2x\mid :2$

$x=8$

 

 

$d)$

${\left(x+1\right)}^2-\left(x+1\right)\left(x-1\right)=12$

$x^2+2x+1-\left(x^2-1\right)=12$

$x^2+2x+1-x^2+1=12$

$2x+2=12\mid -2$

$2x=10\mid :2$

$x=5$