(8-6i)(a+21i)=290

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Solution for (8-6i)(a+21i)=290 equation: 


Simplifying
(8 + -6i)(a + 21i) = 290

Multiply (8 + -6i) * (a + 21i)
(8(a + 21i) + -6i * (a + 21i)) = 290
((a * 8 + 21i * 8) + -6i * (a + 21i)) = 290
((8a + 168i) + -6i * (a + 21i)) = 290
(8a + 168i + (a * -6i + 21i * -6i)) = 290
(8a + 168i + (-6ai + -126i2)) = 290

Reorder the terms:
(8a + -6ai + 168i + -126i2) = 290
(8a + -6ai + 168i + -126i2) = 290

Solving
8a + -6ai + 168i + -126i2 = 290

Solving for variable 'a'.

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

Add '-168i' to each side of the equation.
8a + -6ai + 168i + -168i + -126i2 = 290 + -168i

Combine like terms: 168i + -168i = 0
8a + -6ai + 0 + -126i2 = 290 + -168i
8a + -6ai + -126i2 = 290 + -168i

Add '126i2' to each side of the equation.
8a + -6ai + -126i2 + 126i2 = 290 + -168i + 126i2

Combine like terms: -126i2 + 126i2 = 0
8a + -6ai + 0 = 290 + -168i + 126i2
8a + -6ai = 290 + -168i + 126i2

Reorder the terms:
-290 + 8a + -6ai + 168i + -126i2 = 290 + -168i + 126i2 + -290 + 168i + -126i2

Reorder the terms:
-290 + 8a + -6ai + 168i + -126i2 = 290 + -290 + -168i + 168i + 126i2 + -126i2

Combine like terms: 290 + -290 = 0
-290 + 8a + -6ai + 168i + -126i2 = 0 + -168i + 168i + 126i2 + -126i2
-290 + 8a + -6ai + 168i + -126i2 = -168i + 168i + 126i2 + -126i2

Combine like terms: -168i + 168i = 0
-290 + 8a + -6ai + 168i + -126i2 = 0 + 126i2 + -126i2
-290 + 8a + -6ai + 168i + -126i2 = 126i2 + -126i2

Combine like terms: 126i2 + -126i2 = 0
-290 + 8a + -6ai + 168i + -126i2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-145 + 4a + -3ai + 84i + -63i2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-145 + 4a + -3ai + 84i + -63i2)' equal to zero and attempt to solve:

Simplifying
-145 + 4a + -3ai + 84i + -63i2 = 0

Solving
-145 + 4a + -3ai + 84i + -63i2 = 0

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

Add '145' to each side of the equation.
-145 + 4a + -3ai + 84i + 145 + -63i2 = 0 + 145

Reorder the terms:
-145 + 145 + 4a + -3ai + 84i + -63i2 = 0 + 145

Combine like terms: -145 + 145 = 0
0 + 4a + -3ai + 84i + -63i2 = 0 + 145
4a + -3ai + 84i + -63i2 = 0 + 145

Combine like terms: 0 + 145 = 145
4a + -3ai + 84i + -63i2 = 145

Add '-84i' to each side of the equation.
4a + -3ai + 84i + -84i + -63i2 = 145 + -84i

Combine like terms: 84i + -84i = 0
4a + -3ai + 0 + -63i2 = 145 + -84i
4a + -3ai + -63i2 = 145 + -84i

Add '63i2' to each side of the equation.
4a + -3ai + -63i2 + 63i2 = 145 + -84i + 63i2

Combine like terms: -63i2 + 63i2 = 0
4a + -3ai + 0 = 145 + -84i + 63i2
4a + -3ai = 145 + -84i + 63i2

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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