(5i+5)(6i-1)=

Solution for (5i+5)(6i-1)= equation:

Simplifying
(5i + 5)(6i + -1) = 0

Reorder the terms:
(5 + 5i)(6i + -1) = 0

Reorder the terms:
(5 + 5i)(-1 + 6i) = 0

Multiply (5 + 5i) * (-1 + 6i)
(5(-1 + 6i) + 5i * (-1 + 6i)) = 0
((-1 * 5 + 6i * 5) + 5i * (-1 + 6i)) = 0
((-5 + 30i) + 5i * (-1 + 6i)) = 0
(-5 + 30i + (-1 * 5i + 6i * 5i)) = 0
(-5 + 30i + (-5i + 30i2)) = 0

Combine like terms: 30i + -5i = 25i
(-5 + 25i + 30i2) = 0

Solving
-5 + 25i + 30i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-1 + 5i + 6i2) = 0

Factor a trinomial.
5((-1 + -1i)(1 + -6i)) = 0

Ignore the factor 5.
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 '(1 + -6i)' equal to zero and attempt to solve:

Simplifying
1 + -6i = 0

Solving
1 + -6i = 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 + -6i = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -6i = 0 + -1
-6i = 0 + -1

Combine like terms: 0 + -1 = -1
-6i = -1

Divide each side by '-6'.
i = 0.1666666667

Simplifying
i = 0.1666666667
Solution
i = {-1, 0.1666666667}