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

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

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

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

Combine like terms: 5i + 2i = 7i
(-5 + 7i + -2i2) = 0

Solving
-5 + 7i + -2i2 = 0

Solving for variable 'i'.

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

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

Simplifying
-5 + 2i = 0

Solving
-5 + 2i = 0

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

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

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

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

Divide each side by '2'.
i = 2.5

Simplifying
i = 2.5
Subproblem 2
Set the factor '(1 + -1i)' equal to zero and attempt to solve:

Simplifying
1 + -1i = 0

Solving
1 + -1i = 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 + -1i = 0 + -1

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

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

Divide each side by '-1'.
i = 1

Simplifying
i = 1
Solution
i = {2.5, 1}