-8i(-6i+2)+7(-2+6i)=0

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Solution for -8i(-6i+2)+7(-2+6i)=0 equation: 


Simplifying
-8i(-6i + 2) + 7(-2 + 6i) = 0

Reorder the terms:
-8i(2 + -6i) + 7(-2 + 6i) = 0
(2 * -8i + -6i * -8i) + 7(-2 + 6i) = 0
(-16i + 48i2) + 7(-2 + 6i) = 0
-16i + 48i2 + (-2 * 7 + 6i * 7) = 0
-16i + 48i2 + (-14 + 42i) = 0

Reorder the terms:
-14 + -16i + 42i + 48i2 = 0

Combine like terms: -16i + 42i = 26i
-14 + 26i + 48i2 = 0

Solving
-14 + 26i + 48i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-7 + 13i + 24i2) = 0

Factor a trinomial.
2((-7 + -8i)(1 + -3i)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-7 + -8i)' equal to zero and attempt to solve:

Simplifying
-7 + -8i = 0

Solving
-7 + -8i = 0

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

Add '7' to each side of the equation.
-7 + 7 + -8i = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -8i = 0 + 7
-8i = 0 + 7

Combine like terms: 0 + 7 = 7
-8i = 7

Divide each side by '-8'.
i = -0.875

Simplifying
i = -0.875

Subproblem 2
Set the factor '(1 + -3i)' equal to zero and attempt to solve:

Simplifying
1 + -3i = 0

Solving
1 + -3i = 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 + -3i = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3i = 0 + -1
-3i = 0 + -1

Combine like terms: 0 + -1 = -1
-3i = -1

Divide each side by '-3'.
i = 0.3333333333

Simplifying
i = 0.3333333333
Solution
i = {-0.875, 0.3333333333}

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