(6-7i)(2+5i)=

Solution for (6-7i)(2+5i)= equation:

Simplifying
(6 + -7i)(2 + 5i) = 0

Multiply (6 + -7i) * (2 + 5i)
(6(2 + 5i) + -7i * (2 + 5i)) = 0
((2 * 6 + 5i * 6) + -7i * (2 + 5i)) = 0
((12 + 30i) + -7i * (2 + 5i)) = 0
(12 + 30i + (2 * -7i + 5i * -7i)) = 0
(12 + 30i + (-14i + -35i2)) = 0

Combine like terms: 30i + -14i = 16i
(12 + 16i + -35i2) = 0

Solving
12 + 16i + -35i2 = 0

Solving for variable 'i'.

Factor a trinomial.
(6 + -7i)(2 + 5i) = 0

Subproblem 1
Set the factor '(6 + -7i)' equal to zero and attempt to solve:

Simplifying
6 + -7i = 0

Solving
6 + -7i = 0

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

Add '-6' to each side of the equation.
6 + -6 + -7i = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -7i = 0 + -6
-7i = 0 + -6

Combine like terms: 0 + -6 = -6
-7i = -6

Divide each side by '-7'.
i = 0.8571428571

Simplifying
i = 0.8571428571
Subproblem 2
Set the factor '(2 + 5i)' equal to zero and attempt to solve:

Simplifying
2 + 5i = 0

Solving
2 + 5i = 0

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

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

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

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

Divide each side by '5'.
i = -0.4

Simplifying
i = -0.4
Solution
i = {0.8571428571, -0.4}