(i-4)(3i+7)=0

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Solution for (i-4)(3i+7)=0 equation: 


Simplifying
(i + -4)(3i + 7) = 0

Reorder the terms:
(-4 + i)(3i + 7) = 0

Reorder the terms:
(-4 + i)(7 + 3i) = 0

Multiply (-4 + i) * (7 + 3i)
(-4(7 + 3i) + i(7 + 3i)) = 0
((7 * -4 + 3i * -4) + i(7 + 3i)) = 0
((-28 + -12i) + i(7 + 3i)) = 0
(-28 + -12i + (7 * i + 3i * i)) = 0
(-28 + -12i + (7i + 3i2)) = 0

Combine like terms: -12i + 7i = -5i
(-28 + -5i + 3i2) = 0

Solving
-28 + -5i + 3i2 = 0

Solving for variable 'i'.

Factor a trinomial.
(-7 + -3i)(4 + -1i) = 0


Subproblem 1
Set the factor '(-7 + -3i)' equal to zero and attempt to solve:

Simplifying
-7 + -3i = 0

Solving
-7 + -3i = 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 + -3i = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -3i = 0 + 7
-3i = 0 + 7

Combine like terms: 0 + 7 = 7
-3i = 7

Divide each side by '-3'.
i = -2.333333333

Simplifying
i = -2.333333333

Subproblem 2
Set the factor '(4 + -1i)' equal to zero and attempt to solve:

Simplifying
4 + -1i = 0

Solving
4 + -1i = 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 + -1i = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1i = 0 + -4
-1i = 0 + -4

Combine like terms: 0 + -4 = -4
-1i = -4

Divide each side by '-1'.
i = 4

Simplifying
i = 4
Solution
i = {-2.333333333, 4}

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