(2-3i)(7+4i)=

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Solution for (2-3i)(7+4i)= equation: 


Simplifying
(2 + -3i)(7 + 4i) = 0

Multiply (2 + -3i) * (7 + 4i)
(2(7 + 4i) + -3i * (7 + 4i)) = 0
((7 * 2 + 4i * 2) + -3i * (7 + 4i)) = 0
((14 + 8i) + -3i * (7 + 4i)) = 0
(14 + 8i + (7 * -3i + 4i * -3i)) = 0
(14 + 8i + (-21i + -12i2)) = 0

Combine like terms: 8i + -21i = -13i
(14 + -13i + -12i2) = 0

Solving
14 + -13i + -12i2 = 0

Solving for variable 'i'.

Factor a trinomial.
(2 + -3i)(7 + 4i) = 0


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

Simplifying
2 + -3i = 0

Solving
2 + -3i = 0

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

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

Combine like terms: 2 + -2 = 0
0 + -3i = 0 + -2
-3i = 0 + -2

Combine like terms: 0 + -2 = -2
-3i = -2

Divide each side by '-3'.
i = 0.6666666667

Simplifying
i = 0.6666666667

Subproblem 2
Set the factor '(7 + 4i)' equal to zero and attempt to solve:

Simplifying
7 + 4i = 0

Solving
7 + 4i = 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 + 4i = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 4i = 0 + -7
4i = 0 + -7

Combine like terms: 0 + -7 = -7
4i = -7

Divide each side by '4'.
i = -1.75

Simplifying
i = -1.75
Solution
i = {0.6666666667, -1.75}

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