(i+5)(i-7)=-27

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Solution for (i+5)(i-7)=-27 equation: 


Simplifying
(i + 5)(i + -7) = -27

Reorder the terms:
(5 + i)(i + -7) = -27

Reorder the terms:
(5 + i)(-7 + i) = -27

Multiply (5 + i) * (-7 + i)
(5(-7 + i) + i(-7 + i)) = -27
((-7 * 5 + i * 5) + i(-7 + i)) = -27
((-35 + 5i) + i(-7 + i)) = -27
(-35 + 5i + (-7 * i + i * i)) = -27
(-35 + 5i + (-7i + i2)) = -27

Combine like terms: 5i + -7i = -2i
(-35 + -2i + i2) = -27

Solving
-35 + -2i + i2 = -27

Solving for variable 'i'.

Reorder the terms:
-35 + 27 + -2i + i2 = -27 + 27

Combine like terms: -35 + 27 = -8
-8 + -2i + i2 = -27 + 27

Combine like terms: -27 + 27 = 0
-8 + -2i + i2 = 0

Factor a trinomial.
(-2 + -1i)(4 + -1i) = 0


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

Simplifying
-2 + -1i = 0

Solving
-2 + -1i = 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 + -1i = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1i = 0 + 2
-1i = 0 + 2

Combine like terms: 0 + 2 = 2
-1i = 2

Divide each side by '-1'.
i = -2

Simplifying
i = -2

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, 4}

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