(8+i)(-5+5i)=

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


Simplifying
(8 + i)(-5 + 5i) = 0

Multiply (8 + i) * (-5 + 5i)
(8(-5 + 5i) + i(-5 + 5i)) = 0
((-5 * 8 + 5i * 8) + i(-5 + 5i)) = 0
((-40 + 40i) + i(-5 + 5i)) = 0
(-40 + 40i + (-5 * i + 5i * i)) = 0
(-40 + 40i + (-5i + 5i2)) = 0

Combine like terms: 40i + -5i = 35i
(-40 + 35i + 5i2) = 0

Solving
-40 + 35i + 5i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-8 + 7i + i2) = 0

Factor a trinomial.
5((-8 + -1i)(1 + -1i)) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-8 + -1i)' equal to zero and attempt to solve:

Simplifying
-8 + -1i = 0

Solving
-8 + -1i = 0

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

Add '8' to each side of the equation.
-8 + 8 + -1i = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1i = 0 + 8
-1i = 0 + 8

Combine like terms: 0 + 8 = 8
-1i = 8

Divide each side by '-1'.
i = -8

Simplifying
i = -8

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 = {-8, 1}

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