(2+5i)(-1+5i)=0

Solution for (2+5i)(-1+5i)=0 equation:

Simplifying
(2 + 5i)(-1 + 5i) = 0

Multiply (2 + 5i) * (-1 + 5i)
(2(-1 + 5i) + 5i * (-1 + 5i)) = 0
((-1 * 2 + 5i * 2) + 5i * (-1 + 5i)) = 0
((-2 + 10i) + 5i * (-1 + 5i)) = 0
(-2 + 10i + (-1 * 5i + 5i * 5i)) = 0
(-2 + 10i + (-5i + 25i2)) = 0

Combine like terms: 10i + -5i = 5i
(-2 + 5i + 25i2) = 0

Solving
-2 + 5i + 25i2 = 0

Solving for variable 'i'.

Factor a trinomial.
(-2 + -5i)(1 + -5i) = 0

Subproblem 1
Set the factor '(-2 + -5i)' equal to zero and attempt to solve:

Simplifying
-2 + -5i = 0

Solving
-2 + -5i = 0

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

Add '2' to each side of the equation.
-2 + 2 + -5i = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -5i = 0 + 2
-5i = 0 + 2

Combine like terms: 0 + 2 = 2
-5i = 2

Divide each side by '-5'.
i = -0.4

Simplifying
i = -0.4
Subproblem 2
Set the factor '(1 + -5i)' equal to zero and attempt to solve:

Simplifying
1 + -5i = 0

Solving
1 + -5i = 0

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

Add '-1' to each side of the equation.
1 + -1 + -5i = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -5i = 0 + -1
-5i = 0 + -1

Combine like terms: 0 + -1 = -1
-5i = -1

Divide each side by '-5'.
i = 0.2

Simplifying
i = 0.2
Solution
i = {-0.4, 0.2}