(2+i)(2-i)=0

Solution for (2+i)(2-i)=0 equation:

Simplifying
(2 + i)(2 + -1i) = 0

Multiply (2 + i) * (2 + -1i)
(2(2 + -1i) + i(2 + -1i)) = 0
((2 * 2 + -1i * 2) + i(2 + -1i)) = 0
((4 + -2i) + i(2 + -1i)) = 0
(4 + -2i + (2 * i + -1i * i)) = 0
(4 + -2i + (2i + -1i2)) = 0

Combine like terms: -2i + 2i = 0
(4 + 0 + -1i2) = 0
(4 + -1i2) = 0

Solving
4 + -1i2 = 0

Solving for variable 'i'.

Move all terms containing i to the left, all other terms to the right.

Add '-4' to each side of the equation.
4 + -4 + -1i2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1i2 = 0 + -4
-1i2 = 0 + -4

Combine like terms: 0 + -4 = -4
-1i2 = -4

Divide each side by '-1'.
i2 = 4

Simplifying
i2 = 4

Take the square root of each side:
i = {-2, 2}