(x^2+3x-4)(3+4i)=0

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Solution for (x^2+3x-4)(3+4i)=0 equation:


Simplifying
(x2 + 3x + -4)(3 + 4i) = 0

Reorder the terms:
(-4 + 3x + x2)(3 + 4i) = 0

Multiply (-4 + 3x + x2) * (3 + 4i)
(-4(3 + 4i) + 3x * (3 + 4i) + x2(3 + 4i)) = 0
((3 * -4 + 4i * -4) + 3x * (3 + 4i) + x2(3 + 4i)) = 0
((-12 + -16i) + 3x * (3 + 4i) + x2(3 + 4i)) = 0
(-12 + -16i + (3 * 3x + 4i * 3x) + x2(3 + 4i)) = 0

Reorder the terms:
(-12 + -16i + (12ix + 9x) + x2(3 + 4i)) = 0
(-12 + -16i + (12ix + 9x) + x2(3 + 4i)) = 0
(-12 + -16i + 12ix + 9x + (3 * x2 + 4i * x2)) = 0

Reorder the terms:
(-12 + -16i + 12ix + 9x + (4ix2 + 3x2)) = 0
(-12 + -16i + 12ix + 9x + (4ix2 + 3x2)) = 0

Reorder the terms:
(-12 + -16i + 12ix + 4ix2 + 9x + 3x2) = 0
(-12 + -16i + 12ix + 4ix2 + 9x + 3x2) = 0

Solving
-12 + -16i + 12ix + 4ix2 + 9x + 3x2 = 0

Solving for variable 'i'.

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

Add '12' to each side of the equation.
-12 + -16i + 12ix + 4ix2 + 9x + 12 + 3x2 = 0 + 12

Reorder the terms:
-12 + 12 + -16i + 12ix + 4ix2 + 9x + 3x2 = 0 + 12

Combine like terms: -12 + 12 = 0
0 + -16i + 12ix + 4ix2 + 9x + 3x2 = 0 + 12
-16i + 12ix + 4ix2 + 9x + 3x2 = 0 + 12

Combine like terms: 0 + 12 = 12
-16i + 12ix + 4ix2 + 9x + 3x2 = 12

Add '-9x' to each side of the equation.
-16i + 12ix + 4ix2 + 9x + -9x + 3x2 = 12 + -9x

Combine like terms: 9x + -9x = 0
-16i + 12ix + 4ix2 + 0 + 3x2 = 12 + -9x
-16i + 12ix + 4ix2 + 3x2 = 12 + -9x

Add '-3x2' to each side of the equation.
-16i + 12ix + 4ix2 + 3x2 + -3x2 = 12 + -9x + -3x2

Combine like terms: 3x2 + -3x2 = 0
-16i + 12ix + 4ix2 + 0 = 12 + -9x + -3x2
-16i + 12ix + 4ix2 = 12 + -9x + -3x2

Reorder the terms:
-12 + -16i + 12ix + 4ix2 + 9x + 3x2 = 12 + -9x + -3x2 + -12 + 9x + 3x2

Reorder the terms:
-12 + -16i + 12ix + 4ix2 + 9x + 3x2 = 12 + -12 + -9x + 9x + -3x2 + 3x2

Combine like terms: 12 + -12 = 0
-12 + -16i + 12ix + 4ix2 + 9x + 3x2 = 0 + -9x + 9x + -3x2 + 3x2
-12 + -16i + 12ix + 4ix2 + 9x + 3x2 = -9x + 9x + -3x2 + 3x2

Combine like terms: -9x + 9x = 0
-12 + -16i + 12ix + 4ix2 + 9x + 3x2 = 0 + -3x2 + 3x2
-12 + -16i + 12ix + 4ix2 + 9x + 3x2 = -3x2 + 3x2

Combine like terms: -3x2 + 3x2 = 0
-12 + -16i + 12ix + 4ix2 + 9x + 3x2 = 0

The solution to this equation could not be determined.

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