4i(-3-ti)+7=27-12i

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Solution for 4i(-3-ti)+7=27-12i equation: 


Simplifying
4i(-3 + -1ti) + 7 = 27 + -12i
(-3 * 4i + -1it * 4i) + 7 = 27 + -12i
(-12i + -4i2t) + 7 = 27 + -12i

Reorder the terms:
7 + -12i + -4i2t = 27 + -12i

Add '12i' to each side of the equation.
7 + -12i + 12i + -4i2t = 27 + -12i + 12i

Combine like terms: -12i + 12i = 0
7 + 0 + -4i2t = 27 + -12i + 12i
7 + -4i2t = 27 + -12i + 12i

Combine like terms: -12i + 12i = 0
7 + -4i2t = 27 + 0
7 + -4i2t = 27

Solving
7 + -4i2t = 27

Solving for variable 'i'.

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

Add '-7' to each side of the equation.
7 + -7 + -4i2t = 27 + -7

Combine like terms: 7 + -7 = 0
0 + -4i2t = 27 + -7
-4i2t = 27 + -7

Combine like terms: 27 + -7 = 20
-4i2t = 20

Divide each side by '-4t'.
i2 = -5t-1

Simplifying
i2 = -5t-1

Combine like terms: -5t-1 + 5t-1 = 0
i2 + 5t-1 = 0

Factor out the Greatest Common Factor (GCF), 't-1'.
t-1(i2t + 5) = 0


Subproblem 1
Set the factor 't-1' equal to zero and attempt to solve:

Simplifying
t-1 = 0

Solving
t-1 = 0

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

Add '-1t-1' to each side of the equation.
t-1 + -1t-1 = 0 + -1t-1
Remove the zero:
0 = -1t-1

Simplifying
0 = -1t-1

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 2
Set the factor '(i2t + 5)' equal to zero and attempt to solve:

Simplifying
i2t + 5 = 0

Reorder the terms:
5 + i2t = 0

Solving
5 + i2t = 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 + i2t = 0 + -5

Combine like terms: 5 + -5 = 0
0 + i2t = 0 + -5
i2t = 0 + -5

Combine like terms: 0 + -5 = -5
i2t = -5

Divide each side by 't'.
i2 = -5t-1

Simplifying
i2 = -5t-1

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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