(4+i)-(3-5i)(-2+5i)=

Solution for (4+i)-(3-5i)(-2+5i)= equation:

Simplifying
(4 + i) + -1(3 + -5i)(-2 + 5i) = 0

Remove parenthesis around (4 + i)
4 + i + -1(3 + -5i)(-2 + 5i) = 0

Multiply (3 + -5i) * (-2 + 5i)
4 + i + -1(3(-2 + 5i) + -5i * (-2 + 5i)) = 0
4 + i + -1((-2 * 3 + 5i * 3) + -5i * (-2 + 5i)) = 0
4 + i + -1((-6 + 15i) + -5i * (-2 + 5i)) = 0
4 + i + -1(-6 + 15i + (-2 * -5i + 5i * -5i)) = 0
4 + i + -1(-6 + 15i + (10i + -25i2)) = 0

Combine like terms: 15i + 10i = 25i
4 + i + -1(-6 + 25i + -25i2) = 0
4 + i + (-6 * -1 + 25i * -1 + -25i2 * -1) = 0
4 + i + (6 + -25i + 25i2) = 0

Reorder the terms:
4 + 6 + i + -25i + 25i2 = 0

Combine like terms: 4 + 6 = 10
10 + i + -25i + 25i2 = 0

Combine like terms: i + -25i = -24i
10 + -24i + 25i2 = 0

Solving
10 + -24i + 25i2 = 0

Solving for variable 'i'.

Begin completing the square.  Divide all terms by
25 the coefficient of the squared term: 

Divide each side by '25'.
0.4 + -0.96i + i2 = 0

Move the constant term to the right:

Add '-0.4' to each side of the equation.
0.4 + -0.96i + -0.4 + i2 = 0 + -0.4

Reorder the terms:
0.4 + -0.4 + -0.96i + i2 = 0 + -0.4

Combine like terms: 0.4 + -0.4 = 0.0
0.0 + -0.96i + i2 = 0 + -0.4
-0.96i + i2 = 0 + -0.4

Combine like terms: 0 + -0.4 = -0.4
-0.96i + i2 = -0.4

The i term is -0.96i.  Take half its coefficient (-0.48).
Square it (0.2304) and add it to both sides.

Add '0.2304' to each side of the equation.
-0.96i + 0.2304 + i2 = -0.4 + 0.2304

Reorder the terms:
0.2304 + -0.96i + i2 = -0.4 + 0.2304

Combine like terms: -0.4 + 0.2304 = -0.1696
0.2304 + -0.96i + i2 = -0.1696

Factor a perfect square on the left side:
(i + -0.48)(i + -0.48) = -0.1696

Can't calculate square root of the right side.

The solution to this equation could not be determined.