(2h-3i)(h+4i)=

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


Simplifying
(2h + -3i)(h + 4i) = 0

Multiply (2h + -3i) * (h + 4i)
(2h * (h + 4i) + -3i * (h + 4i)) = 0
((h * 2h + 4i * 2h) + -3i * (h + 4i)) = 0

Reorder the terms:
((8hi + 2h2) + -3i * (h + 4i)) = 0
((8hi + 2h2) + -3i * (h + 4i)) = 0
(8hi + 2h2 + (h * -3i + 4i * -3i)) = 0
(8hi + 2h2 + (-3hi + -12i2)) = 0

Reorder the terms:
(8hi + -3hi + 2h2 + -12i2) = 0

Combine like terms: 8hi + -3hi = 5hi
(5hi + 2h2 + -12i2) = 0

Solving
5hi + 2h2 + -12i2 = 0

Solving for variable 'h'.

Factor a trinomial.
(2h + -3i)(h + 4i) = 0


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

Simplifying
2h + -3i = 0

Solving
2h + -3i = 0

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

Add '3i' to each side of the equation.
2h + -3i + 3i = 0 + 3i

Combine like terms: -3i + 3i = 0
2h + 0 = 0 + 3i
2h = 0 + 3i
Remove the zero:
2h = 3i

Divide each side by '2'.
h = 1.5i

Simplifying
h = 1.5i

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

Simplifying
h + 4i = 0

Solving
h + 4i = 0

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

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

Combine like terms: 4i + -4i = 0
h + 0 = 0 + -4i
h = 0 + -4i
Remove the zero:
h = -4i

Simplifying
h = -4i
Solution
h = {1.5i, -4i}

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