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

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


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

Reorder the terms:
(-4 + 3i)(3i + 5) = 0

Reorder the terms:
(-4 + 3i)(5 + 3i) = 0

Multiply (-4 + 3i) * (5 + 3i)
(-4(5 + 3i) + 3i * (5 + 3i)) = 0
((5 * -4 + 3i * -4) + 3i * (5 + 3i)) = 0
((-20 + -12i) + 3i * (5 + 3i)) = 0
(-20 + -12i + (5 * 3i + 3i * 3i)) = 0
(-20 + -12i + (15i + 9i2)) = 0

Combine like terms: -12i + 15i = 3i
(-20 + 3i + 9i2) = 0

Solving
-20 + 3i + 9i2 = 0

Solving for variable 'i'.

Factor a trinomial.
(-5 + -3i)(4 + -3i) = 0


Subproblem 1
Set the factor '(-5 + -3i)' equal to zero and attempt to solve:

Simplifying
-5 + -3i = 0

Solving
-5 + -3i = 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 + -3i = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -3i = 0 + 5
-3i = 0 + 5

Combine like terms: 0 + 5 = 5
-3i = 5

Divide each side by '-3'.
i = -1.666666667

Simplifying
i = -1.666666667

Subproblem 2
Set the factor '(4 + -3i)' equal to zero and attempt to solve:

Simplifying
4 + -3i = 0

Solving
4 + -3i = 0

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

Add '-4' to each side of the equation.
4 + -4 + -3i = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -3i = 0 + -4
-3i = 0 + -4

Combine like terms: 0 + -4 = -4
-3i = -4

Divide each side by '-3'.
i = 1.333333333

Simplifying
i = 1.333333333
Solution
i = {-1.666666667, 1.333333333}

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