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

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


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

Multiply (-2 + -5i) * (7 + 2i)
(-2(7 + 2i) + -5i * (7 + 2i)) = 0
((7 * -2 + 2i * -2) + -5i * (7 + 2i)) = 0
((-14 + -4i) + -5i * (7 + 2i)) = 0
(-14 + -4i + (7 * -5i + 2i * -5i)) = 0
(-14 + -4i + (-35i + -10i2)) = 0

Combine like terms: -4i + -35i = -39i
(-14 + -39i + -10i2) = 0

Solving
-14 + -39i + -10i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(14 + 39i + 10i2) = 0

Factor a trinomial.
-1((7 + 2i)(2 + 5i)) = 0

Ignore the factor -1.

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

Simplifying
7 + 2i = 0

Solving
7 + 2i = 0

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

Add '-7' to each side of the equation.
7 + -7 + 2i = 0 + -7

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

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

Divide each side by '2'.
i = -3.5

Simplifying
i = -3.5

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 = {-3.5, -0.4}

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