=(2-7i)(-1+4i)

Solution for =(2-7i)(-1+4i) equation:

Simplifying
0 = (2 + -7i)(-1 + 4i)

Multiply (2 + -7i) * (-1 + 4i)
0 = (2(-1 + 4i) + -7i * (-1 + 4i))
0 = ((-1 * 2 + 4i * 2) + -7i * (-1 + 4i))
0 = ((-2 + 8i) + -7i * (-1 + 4i))
0 = (-2 + 8i + (-1 * -7i + 4i * -7i))
0 = (-2 + 8i + (7i + -28i2))

Combine like terms: 8i + 7i = 15i
0 = (-2 + 15i + -28i2)

Solving
0 = -2 + 15i + -28i2

Solving for variable 'i'.

Combine like terms: 0 + 2 = 2
2 + -15i + 28i2 = -2 + 15i + -28i2 + 2 + -15i + 28i2

Reorder the terms:
2 + -15i + 28i2 = -2 + 2 + 15i + -15i + -28i2 + 28i2

Combine like terms: -2 + 2 = 0
2 + -15i + 28i2 = 0 + 15i + -15i + -28i2 + 28i2
2 + -15i + 28i2 = 15i + -15i + -28i2 + 28i2

Combine like terms: 15i + -15i = 0
2 + -15i + 28i2 = 0 + -28i2 + 28i2
2 + -15i + 28i2 = -28i2 + 28i2

Combine like terms: -28i2 + 28i2 = 0
2 + -15i + 28i2 = 0

Factor a trinomial.
(1 + -4i)(2 + -7i) = 0

Subproblem 1
Set the factor '(1 + -4i)' equal to zero and attempt to solve:

Simplifying
1 + -4i = 0

Solving
1 + -4i = 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 + -4i = 0 + -1

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

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

Divide each side by '-4'.
i = 0.25

Simplifying
i = 0.25
Subproblem 2
Set the factor '(2 + -7i)' equal to zero and attempt to solve:

Simplifying
2 + -7i = 0

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

Combine like terms: 2 + -2 = 0
0 + -7i = 0 + -2
-7i = 0 + -2

Combine like terms: 0 + -2 = -2
-7i = -2

Divide each side by '-7'.
i = 0.2857142857

Simplifying
i = 0.2857142857
Solution
i = {0.25, 0.2857142857}