3a+(4b+2)I=a-6i

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Solution for 3a+(4b+2)I=a-6i equation:


Simplifying
3a + (4b + 2) * I = a + -6i

Reorder the terms:
3a + (2 + 4b) * I = a + -6i

Reorder the terms for easier multiplication:
3a + I(2 + 4b) = a + -6i
3a + (2 * I + 4b * I) = a + -6i
3a + (2I + 4bI) = a + -6i

Reorder the terms:
2I + 3a + 4bI = a + -6i

Solving
2I + 3a + 4bI = a + -6i

Solving for variable 'I'.

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

Add '-3a' to each side of the equation.
2I + 3a + -3a + 4bI = a + -3a + -6i

Combine like terms: 3a + -3a = 0
2I + 0 + 4bI = a + -3a + -6i
2I + 4bI = a + -3a + -6i

Combine like terms: a + -3a = -2a
2I + 4bI = -2a + -6i

Reorder the terms:
2I + 2a + 4bI + 6i = -2a + -6i + 2a + 6i

Reorder the terms:
2I + 2a + 4bI + 6i = -2a + 2a + -6i + 6i

Combine like terms: -2a + 2a = 0
2I + 2a + 4bI + 6i = 0 + -6i + 6i
2I + 2a + 4bI + 6i = -6i + 6i

Combine like terms: -6i + 6i = 0
2I + 2a + 4bI + 6i = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(I + a + 2bI + 3i) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(I + a + 2bI + 3i)' equal to zero and attempt to solve: Simplifying I + a + 2bI + 3i = 0 Solving I + a + 2bI + 3i = 0 Move all terms containing I to the left, all other terms to the right. Add '-1a' to each side of the equation. I + a + 2bI + -1a + 3i = 0 + -1a Reorder the terms: I + a + -1a + 2bI + 3i = 0 + -1a Combine like terms: a + -1a = 0 I + 0 + 2bI + 3i = 0 + -1a I + 2bI + 3i = 0 + -1a Remove the zero: I + 2bI + 3i = -1a Add '-3i' to each side of the equation. I + 2bI + 3i + -3i = -1a + -3i Combine like terms: 3i + -3i = 0 I + 2bI + 0 = -1a + -3i I + 2bI = -1a + -3i 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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