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

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

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

Multiply (6 + 2i) * (2 + -7i)
(6(2 + -7i) + 2i * (2 + -7i)) = 0
((2 * 6 + -7i * 6) + 2i * (2 + -7i)) = 0
((12 + -42i) + 2i * (2 + -7i)) = 0
(12 + -42i + (2 * 2i + -7i * 2i)) = 0
(12 + -42i + (4i + -14i2)) = 0

Combine like terms: -42i + 4i = -38i
(12 + -38i + -14i2) = 0

Solving
12 + -38i + -14i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '2'.
2(6 + -19i + -7i2) = 0

Factor a trinomial.
2((2 + -7i)(3 + i)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(2 + -7i)' equal to zero and attempt to solve:

Simplifying
2 + -7i = 0

Solving
2 + -7i = 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 + -7i = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -7i = 0 + -2
-7i = 0 + -2

Combine like terms: 0 + -2 = -2
-7i = -2

Divide each side by '-7'.
i = 0.2857142857

Simplifying
i = 0.2857142857
Subproblem 2
Set the factor '(3 + i)' equal to zero and attempt to solve:

Simplifying
3 + i = 0

Solving
3 + i = 0

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

Add '-3' to each side of the equation.
3 + -3 + i = 0 + -3

Combine like terms: 3 + -3 = 0
0 + i = 0 + -3
i = 0 + -3

Combine like terms: 0 + -3 = -3
i = -3

Simplifying
i = -3
Solution
i = {0.2857142857, -3}