$\text{a)}$  

$\left(x+2\right)\left(x-3\right)=x^2+4$  

$x^2-3x+2x-6=x^2+4\mid -x^2+6$      

$-x=10\mid :\left(-1\right)$  

$x=-10$  

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$\text{b)}$  

$\left(x-4\right)\left(x+6\right)=x\left(x-4\right)$  

$x^2+6x-4x-24=x^2-4x\mid -x^2+4x+24$  

$6x=24\mid :6$  

$x=4$  

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$\text{c)}$  

$\left(x-2\right)\left(x-5\right)=\left(x+3\right)\left(x+6\right)$  

$x^2-5x-2x+10=x^2+6x+3x+18\mid -x^2$  

$-7x+10=9x+18\mid -9x-10$  

$-16x=8\mid :\left(-16\right)$  

$x=-\frac{1}{2}$  

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$\text{d)}$  

$\left(2x+1\right)\left(x+3\right)=\left(x-4\right)\left(2x-3\right)$  

$2x^2+6x+1x+3=2x^2-3x-8x+12\mid -2x^2$  

$7x+3=-11x+12\mid +11x-3$  

$18x=9\mid :18$  

$x=\frac{1}{2}$