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

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Solution for i-(5-4i)(-2+3i)=0 equation: 


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

Multiply (5 + -4i) * (-2 + 3i)
i + -1(5(-2 + 3i) + -4i * (-2 + 3i)) = 0
i + -1((-2 * 5 + 3i * 5) + -4i * (-2 + 3i)) = 0
i + -1((-10 + 15i) + -4i * (-2 + 3i)) = 0
i + -1(-10 + 15i + (-2 * -4i + 3i * -4i)) = 0
i + -1(-10 + 15i + (8i + -12i2)) = 0

Combine like terms: 15i + 8i = 23i
i + -1(-10 + 23i + -12i2) = 0
i + (-10 * -1 + 23i * -1 + -12i2 * -1) = 0
i + (10 + -23i + 12i2) = 0

Reorder the terms:
10 + i + -23i + 12i2 = 0

Combine like terms: i + -23i = -22i
10 + -22i + 12i2 = 0

Solving
10 + -22i + 12i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '2'.
2(5 + -11i + 6i2) = 0

Factor a trinomial.
2((5 + -6i)(1 + -1i)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(5 + -6i)' equal to zero and attempt to solve:

Simplifying
5 + -6i = 0

Solving
5 + -6i = 0

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

Add '-5' to each side of the equation.
5 + -5 + -6i = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -6i = 0 + -5
-6i = 0 + -5

Combine like terms: 0 + -5 = -5
-6i = -5

Divide each side by '-6'.
i = 0.8333333333

Simplifying
i = 0.8333333333

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 = {0.8333333333, 1}

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