3(I-3)7(I+3)=4(2I-3)-8(2I+3)

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Solution for 3(I-3)7(I+3)=4(2I-3)-8(2I+3) equation:


Simplifying
3(I + -3) * 7(I + 3) = 4(2I + -3) + -8(2I + 3)

Reorder the terms:
3(-3 + I) * 7(I + 3) = 4(2I + -3) + -8(2I + 3)

Reorder the terms:
3(-3 + I) * 7(3 + I) = 4(2I + -3) + -8(2I + 3)

Reorder the terms for easier multiplication:
3 * 7(-3 + I)(3 + I) = 4(2I + -3) + -8(2I + 3)

Multiply 3 * 7
21(-3 + I)(3 + I) = 4(2I + -3) + -8(2I + 3)

Multiply (-3 + I) * (3 + I)
21(-3(3 + I) + I(3 + I)) = 4(2I + -3) + -8(2I + 3)
21((3 * -3 + I * -3) + I(3 + I)) = 4(2I + -3) + -8(2I + 3)
21((-9 + -3I) + I(3 + I)) = 4(2I + -3) + -8(2I + 3)
21(-9 + -3I + (3 * I + I * I)) = 4(2I + -3) + -8(2I + 3)
21(-9 + -3I + (3I + I2)) = 4(2I + -3) + -8(2I + 3)

Combine like terms: -3I + 3I = 0
21(-9 + 0 + I2) = 4(2I + -3) + -8(2I + 3)
21(-9 + I2) = 4(2I + -3) + -8(2I + 3)
(-9 * 21 + I2 * 21) = 4(2I + -3) + -8(2I + 3)
(-189 + 21I2) = 4(2I + -3) + -8(2I + 3)

Reorder the terms:
-189 + 21I2 = 4(-3 + 2I) + -8(2I + 3)
-189 + 21I2 = (-3 * 4 + 2I * 4) + -8(2I + 3)
-189 + 21I2 = (-12 + 8I) + -8(2I + 3)

Reorder the terms:
-189 + 21I2 = -12 + 8I + -8(3 + 2I)
-189 + 21I2 = -12 + 8I + (3 * -8 + 2I * -8)
-189 + 21I2 = -12 + 8I + (-24 + -16I)

Reorder the terms:
-189 + 21I2 = -12 + -24 + 8I + -16I

Combine like terms: -12 + -24 = -36
-189 + 21I2 = -36 + 8I + -16I

Combine like terms: 8I + -16I = -8I
-189 + 21I2 = -36 + -8I

Solving
-189 + 21I2 = -36 + -8I

Solving for variable 'I'.

Reorder the terms:
-189 + 36 + 8I + 21I2 = -36 + -8I + 36 + 8I

Combine like terms: -189 + 36 = -153
-153 + 8I + 21I2 = -36 + -8I + 36 + 8I

Reorder the terms:
-153 + 8I + 21I2 = -36 + 36 + -8I + 8I

Combine like terms: -36 + 36 = 0
-153 + 8I + 21I2 = 0 + -8I + 8I
-153 + 8I + 21I2 = -8I + 8I

Combine like terms: -8I + 8I = 0
-153 + 8I + 21I2 = 0

Begin completing the square.  Divide all terms by
21 the coefficient of the squared term: 

Divide each side by '21'.
-7.285714286 + 0.380952381I + I2 = 0

Move the constant term to the right:

Add '7.285714286' to each side of the equation.
-7.285714286 + 0.380952381I + 7.285714286 + I2 = 0 + 7.285714286

Reorder the terms:
-7.285714286 + 7.285714286 + 0.380952381I + I2 = 0 + 7.285714286

Combine like terms: -7.285714286 + 7.285714286 = 0.000000000
0.000000000 + 0.380952381I + I2 = 0 + 7.285714286
0.380952381I + I2 = 0 + 7.285714286

Combine like terms: 0 + 7.285714286 = 7.285714286
0.380952381I + I2 = 7.285714286

The I term is 0.380952381I.  Take half its coefficient (0.1904761905).
Square it (0.03628117915) and add it to both sides.

Add '0.03628117915' to each side of the equation.
0.380952381I + 0.03628117915 + I2 = 7.285714286 + 0.03628117915

Reorder the terms:
0.03628117915 + 0.380952381I + I2 = 7.285714286 + 0.03628117915

Combine like terms: 7.285714286 + 0.03628117915 = 7.32199546515
0.03628117915 + 0.380952381I + I2 = 7.32199546515

Factor a perfect square on the left side:
(I + 0.1904761905)(I + 0.1904761905) = 7.32199546515

Calculate the square root of the right side: 2.705918599

Break this problem into two subproblems by setting 
(I + 0.1904761905) equal to 2.705918599 and -2.705918599.

Subproblem 1

I + 0.1904761905 = 2.705918599 Simplifying I + 0.1904761905 = 2.705918599 Reorder the terms: 0.1904761905 + I = 2.705918599 Solving 0.1904761905 + I = 2.705918599 Solving for variable 'I'. Move all terms containing I to the left, all other terms to the right. Add '-0.1904761905' to each side of the equation. 0.1904761905 + -0.1904761905 + I = 2.705918599 + -0.1904761905 Combine like terms: 0.1904761905 + -0.1904761905 = 0.0000000000 0.0000000000 + I = 2.705918599 + -0.1904761905 I = 2.705918599 + -0.1904761905 Combine like terms: 2.705918599 + -0.1904761905 = 2.5154424085 I = 2.5154424085 Simplifying I = 2.5154424085

Subproblem 2

I + 0.1904761905 = -2.705918599 Simplifying I + 0.1904761905 = -2.705918599 Reorder the terms: 0.1904761905 + I = -2.705918599 Solving 0.1904761905 + I = -2.705918599 Solving for variable 'I'. Move all terms containing I to the left, all other terms to the right. Add '-0.1904761905' to each side of the equation. 0.1904761905 + -0.1904761905 + I = -2.705918599 + -0.1904761905 Combine like terms: 0.1904761905 + -0.1904761905 = 0.0000000000 0.0000000000 + I = -2.705918599 + -0.1904761905 I = -2.705918599 + -0.1904761905 Combine like terms: -2.705918599 + -0.1904761905 = -2.8963947895 I = -2.8963947895 Simplifying I = -2.8963947895

Solution

The solution to the problem is based on the solutions from the subproblems. I = {2.5154424085, -2.8963947895}

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