2(x+1)(x-4)-(x-2)^2 = 0 FOIL -->

2[x^2 -3x -4] -[x^2 -4x +4] = 0

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

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

x^2 -2x -12 = 0 Quadratic equation from here with a = 1, b = -2, c = -12

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(x-1)(x+2)=18 FOIL -->

x^2 +x -2 = 18 Set equal to zero [standard form for quadratics] -->

x^2 +x -20 = 0 Factor -->

(x+5)(x-4) = 0 Set each factor equal to zero and solve.