(12a-4b)i+a+5b=15+58i

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Solution for (12a-4b)i+a+5b=15+58i equation: 


Simplifying
(12a + -4b) * i + a + 5b = 15 + 58i

Reorder the terms for easier multiplication:
i(12a + -4b) + a + 5b = 15 + 58i
(12a * i + -4b * i) + a + 5b = 15 + 58i
(12ai + -4bi) + a + 5b = 15 + 58i

Reorder the terms:
a + 12ai + 5b + -4bi = 15 + 58i

Solving
a + 12ai + 5b + -4bi = 15 + 58i

Solving for variable 'a'.

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

Add '-5b' to each side of the equation.
a + 12ai + 5b + -5b + -4bi = 15 + -5b + 58i

Combine like terms: 5b + -5b = 0
a + 12ai + 0 + -4bi = 15 + -5b + 58i
a + 12ai + -4bi = 15 + -5b + 58i

Add '4bi' to each side of the equation.
a + 12ai + -4bi + 4bi = 15 + -5b + 4bi + 58i

Combine like terms: -4bi + 4bi = 0
a + 12ai + 0 = 15 + -5b + 4bi + 58i
a + 12ai = 15 + -5b + 4bi + 58i

Reorder the terms:
-15 + a + 12ai + 5b + -4bi + -58i = 15 + -5b + 4bi + 58i + -15 + 5b + -4bi + -58i

Reorder the terms:
-15 + a + 12ai + 5b + -4bi + -58i = 15 + -15 + -5b + 5b + 4bi + -4bi + 58i + -58i

Combine like terms: 15 + -15 = 0
-15 + a + 12ai + 5b + -4bi + -58i = 0 + -5b + 5b + 4bi + -4bi + 58i + -58i
-15 + a + 12ai + 5b + -4bi + -58i = -5b + 5b + 4bi + -4bi + 58i + -58i

Combine like terms: -5b + 5b = 0
-15 + a + 12ai + 5b + -4bi + -58i = 0 + 4bi + -4bi + 58i + -58i
-15 + a + 12ai + 5b + -4bi + -58i = 4bi + -4bi + 58i + -58i

Combine like terms: 4bi + -4bi = 0
-15 + a + 12ai + 5b + -4bi + -58i = 0 + 58i + -58i
-15 + a + 12ai + 5b + -4bi + -58i = 58i + -58i

Combine like terms: 58i + -58i = 0
-15 + a + 12ai + 5b + -4bi + -58i = 0

The solution to this equation could not be determined.

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