Solve for x: 4^(x^2+x)-4096=0.

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We have to determine the value of x for the equation: 4^(x^2+x) - 4096 = 0.

4^(x^2+x) - 4096 = 0

=> 4^(x^2+x) = 4096

=> 4^(x^2+x) = 4096

=> 4^(x^2+x) = 4^6

As the base is equal, equate the exponent

=> x^2 + x = 6

=> x^2 + 3x - 2x - 6 = 0

=> x(x + 3) - 2(x + 3) = 0

=> (x - 2)(x + 3) = 0

=> x = 2 and x = -3

The required values are x = 2 and x = -3

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