15-3(-3+5i)=i(5+2(-3+5i))

Solution for 15-3(-3+5i)=i(5+2(-3+5i)) equation:

Simplifying
15 + -3(-3 + 5i) = i(5 + 2(-3 + 5i))
15 + (-3 * -3 + 5i * -3) = i(5 + 2(-3 + 5i))
15 + (9 + -15i) = i(5 + 2(-3 + 5i))

Combine like terms: 15 + 9 = 24
24 + -15i = i(5 + 2(-3 + 5i))
24 + -15i = i(5 + (-3 * 2 + 5i * 2))
24 + -15i = i(5 + (-6 + 10i))

Combine like terms: 5 + -6 = -1
24 + -15i = i(-1 + 10i)
24 + -15i = (-1 * i + 10i * i)
24 + -15i = (-1i + 10i2)

Solving
24 + -15i = -1i + 10i2

Solving for variable 'i'.

Combine like terms: -15i + i = -14i
24 + -14i + -10i2 = -1i + 10i2 + i + -10i2

Reorder the terms:
24 + -14i + -10i2 = -1i + i + 10i2 + -10i2

Combine like terms: -1i + i = 0
24 + -14i + -10i2 = 0 + 10i2 + -10i2
24 + -14i + -10i2 = 10i2 + -10i2

Combine like terms: 10i2 + -10i2 = 0
24 + -14i + -10i2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(12 + -7i + -5i2) = 0

Factor a trinomial.
2((1 + -1i)(12 + 5i)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(1 + -1i)' equal to zero and attempt to solve:

Simplifying
1 + -1i = 0

Solving
1 + -1i = 0

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

Add '-1' to each side of the equation.
1 + -1 + -1i = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1i = 0 + -1
-1i = 0 + -1

Combine like terms: 0 + -1 = -1
-1i = -1

Divide each side by '-1'.
i = 1

Simplifying
i = 1
Subproblem 2
Set the factor '(12 + 5i)' equal to zero and attempt to solve:

Simplifying
12 + 5i = 0

Solving
12 + 5i = 0

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

Add '-12' to each side of the equation.
12 + -12 + 5i = 0 + -12

Combine like terms: 12 + -12 = 0
0 + 5i = 0 + -12
5i = 0 + -12

Combine like terms: 0 + -12 = -12
5i = -12

Divide each side by '5'.
i = -2.4

Simplifying
i = -2.4
Solution
i = {1, -2.4}