(2i+2)(2i+5)=

Solution for (2i+2)(2i+5)= equation:

Simplifying
(2i + 2)(2i + 5) = 0

Reorder the terms:
(2 + 2i)(2i + 5) = 0

Reorder the terms:
(2 + 2i)(5 + 2i) = 0

Multiply (2 + 2i) * (5 + 2i)
(2(5 + 2i) + 2i * (5 + 2i)) = 0
((5 * 2 + 2i * 2) + 2i * (5 + 2i)) = 0
((10 + 4i) + 2i * (5 + 2i)) = 0
(10 + 4i + (5 * 2i + 2i * 2i)) = 0
(10 + 4i + (10i + 4i2)) = 0

Combine like terms: 4i + 10i = 14i
(10 + 14i + 4i2) = 0

Solving
10 + 14i + 4i2 = 0

Solving for variable 'i'.

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

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

Ignore the factor 2.
Subproblem 1
Set the factor '(5 + 2i)' equal to zero and attempt to solve:

Simplifying
5 + 2i = 0

Solving
5 + 2i = 0

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

Add '-5' to each side of the equation.
5 + -5 + 2i = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 2i = 0 + -5
2i = 0 + -5

Combine like terms: 0 + -5 = -5
2i = -5

Divide each side by '2'.
i = -2.5

Simplifying
i = -2.5
Subproblem 2
Set the factor '(1 + i)' equal to zero and attempt to solve:

Simplifying
1 + i = 0

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

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

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

Simplifying
i = -1
Solution
i = {-2.5, -1}