3i(5+2i)-2(5-4i)=0

Simple and best practice solution for 3i(5+2i)-2(5-4i)=0 equation. Check how easy it is, and learn it for the future. Our solution is simple, and easy to understand, so don`t hesitate to use it as a solution of your homework.

If it's not what You are looking for type in the equation solver your own equation and let us solve it.

Solution for 3i(5+2i)-2(5-4i)=0 equation: 


Simplifying
3i(5 + 2i) + -2(5 + -4i) = 0
(5 * 3i + 2i * 3i) + -2(5 + -4i) = 0
(15i + 6i2) + -2(5 + -4i) = 0
15i + 6i2 + (5 * -2 + -4i * -2) = 0
15i + 6i2 + (-10 + 8i) = 0

Reorder the terms:
-10 + 15i + 8i + 6i2 = 0

Combine like terms: 15i + 8i = 23i
-10 + 23i + 6i2 = 0

Solving
-10 + 23i + 6i2 = 0

Solving for variable 'i'.

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

Divide each side by '6'.
-1.666666667 + 3.833333333i + i2 = 0

Move the constant term to the right:

Add '1.666666667' to each side of the equation.
-1.666666667 + 3.833333333i + 1.666666667 + i2 = 0 + 1.666666667

Reorder the terms:
-1.666666667 + 1.666666667 + 3.833333333i + i2 = 0 + 1.666666667

Combine like terms: -1.666666667 + 1.666666667 = 0.000000000
0.000000000 + 3.833333333i + i2 = 0 + 1.666666667
3.833333333i + i2 = 0 + 1.666666667

Combine like terms: 0 + 1.666666667 = 1.666666667
3.833333333i + i2 = 1.666666667

The i term is 3.833333333i.  Take half its coefficient (1.916666667).
Square it (3.673611112) and add it to both sides.

Add '3.673611112' to each side of the equation.
3.833333333i + 3.673611112 + i2 = 1.666666667 + 3.673611112

Reorder the terms:
3.673611112 + 3.833333333i + i2 = 1.666666667 + 3.673611112

Combine like terms: 1.666666667 + 3.673611112 = 5.340277779
3.673611112 + 3.833333333i + i2 = 5.340277779

Factor a perfect square on the left side:
(i + 1.916666667)(i + 1.916666667) = 5.340277779

Calculate the square root of the right side: 2.310904104

Break this problem into two subproblems by setting 
(i + 1.916666667) equal to 2.310904104 and -2.310904104.


Subproblem 1
i + 1.916666667 = 2.310904104

Simplifying
i + 1.916666667 = 2.310904104

Reorder the terms:
1.916666667 + i = 2.310904104

Solving
1.916666667 + i = 2.310904104

Solving for variable 'i'.

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

Add '-1.916666667' to each side of the equation.
1.916666667 + -1.916666667 + i = 2.310904104 + -1.916666667

Combine like terms: 1.916666667 + -1.916666667 = 0.000000000
0.000000000 + i = 2.310904104 + -1.916666667
i = 2.310904104 + -1.916666667

Combine like terms: 2.310904104 + -1.916666667 = 0.394237437
i = 0.394237437

Simplifying
i = 0.394237437


Subproblem 2
i + 1.916666667 = -2.310904104

Simplifying
i + 1.916666667 = -2.310904104

Reorder the terms:
1.916666667 + i = -2.310904104

Solving
1.916666667 + i = -2.310904104

Solving for variable 'i'.

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

Add '-1.916666667' to each side of the equation.
1.916666667 + -1.916666667 + i = -2.310904104 + -1.916666667

Combine like terms: 1.916666667 + -1.916666667 = 0.000000000
0.000000000 + i = -2.310904104 + -1.916666667
i = -2.310904104 + -1.916666667

Combine like terms: -2.310904104 + -1.916666667 = -4.227570771
i = -4.227570771

Simplifying
i = -4.227570771


Solution
The solution to the problem is based on the solutions
from the subproblems.
i = {0.394237437, -4.227570771}

See similar equations:

| -7+11g=9-11g | | 70+2x=68+1.5x | | X+2=6x+22 | | X+12=140 | | -(x+8)(x-5)=0 | | -(x^5-20x^3+64x)=0 | | 12x-47+5=18 | | (8/9)-5)3 | | -2(-3x-8)=58 | | xy-5xy^2= | | 21=-18 | | h3/h-6 | | 4x+14-6x+22=4 | | 3y^2-20y+15=0 | | -x+9=-5x+57 | | (-x+9i)(x-9i)=0 | | 5/(x-3)-6=12/(x-3) | | 7x+2=2x+1 | | 116=121-x | | 5-3/12 | | 3=-4(1)+b | | a^2+9=9 | | 39-4a=7+6(1-5a) | | 2/5h=28 | | Y^4+16y=-1 | | -6x-(-6)-7=-7x+7 | | (-x-9i)(x-9i)=0 | | -38=-18-9 | | F(x)=1n(x-2)-4 | | x(3)+9=27 | | X^2+3=5x(x+6) | | 4(3+m)=8(6m+7) |

Equations solver categories