(5i+2)(5i-2)=0

Solution for (5i+2)(5i-2)=0 equation:

Simplifying
(5i + 2)(5i + -2) = 0

Reorder the terms:
(2 + 5i)(5i + -2) = 0

Reorder the terms:
(2 + 5i)(-2 + 5i) = 0

Multiply (2 + 5i) * (-2 + 5i)
(2(-2 + 5i) + 5i * (-2 + 5i)) = 0
((-2 * 2 + 5i * 2) + 5i * (-2 + 5i)) = 0
((-4 + 10i) + 5i * (-2 + 5i)) = 0
(-4 + 10i + (-2 * 5i + 5i * 5i)) = 0
(-4 + 10i + (-10i + 25i2)) = 0

Combine like terms: 10i + -10i = 0
(-4 + 0 + 25i2) = 0
(-4 + 25i2) = 0

Solving
-4 + 25i2 = 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 + 25i2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + 25i2 = 0 + 4
25i2 = 0 + 4

Combine like terms: 0 + 4 = 4
25i2 = 4

Divide each side by '25'.
i2 = 0.16

Simplifying
i2 = 0.16

Take the square root of each side:
i = {-0.4, 0.4}