(2-5i)(-2+7i)=(2-2)(-6+8)i

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Solution for (2-5i)(-2+7i)=(2-2)(-6+8)i equation: 


Simplifying
(2 + -5i)(-2 + 7i) = (2 + -2)(-6 + 8) * i

Multiply (2 + -5i) * (-2 + 7i)
(2(-2 + 7i) + -5i * (-2 + 7i)) = (2 + -2)(-6 + 8) * i
((-2 * 2 + 7i * 2) + -5i * (-2 + 7i)) = (2 + -2)(-6 + 8) * i
((-4 + 14i) + -5i * (-2 + 7i)) = (2 + -2)(-6 + 8) * i
(-4 + 14i + (-2 * -5i + 7i * -5i)) = (2 + -2)(-6 + 8) * i
(-4 + 14i + (10i + -35i2)) = (2 + -2)(-6 + 8) * i

Combine like terms: 14i + 10i = 24i
(-4 + 24i + -35i2) = (2 + -2)(-6 + 8) * i

Combine like terms: 2 + -2 = 0
-4 + 24i + -35i2 = (0)(-6 + 8) * i

Combine like terms: -6 + 8 = 2
-4 + 24i + -35i2 = 0(2) * i

Multiply 0 * 2
-4 + 24i + -35i2 = 0i

Anything times zero is zero.
-4 + 24i + -35i2 = 0i

Solving
-4 + 24i + -35i2 = 0

Solving for variable 'i'.

Factor a trinomial.
(-2 + 5i)(2 + -7i) = 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 '(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 = {0.4, 0.2857142857}

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