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

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


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

Remove parenthesis around (-5i)
-5i(-7 + -6i)(2 + i) = 0

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

Combine like terms: -7i + -12i = -19i
-5i(-14 + -19i + -6i2) = 0
(-14 * -5i + -19i * -5i + -6i2 * -5i) = 0
(70i + 95i2 + 30i3) = 0

Solving
70i + 95i2 + 30i3 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '5i'.
5i(14 + 19i + 6i2) = 0

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

Ignore the factor 5.

Subproblem 1
Set the factor 'i' equal to zero and attempt to solve:

Simplifying
i = 0

Solving
i = 0

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

Simplifying
i = 0

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

Simplifying
2 + i = 0

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

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

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

Simplifying
i = -2

Subproblem 3
Set the factor '(7 + 6i)' equal to zero and attempt to solve:

Simplifying
7 + 6i = 0

Solving
7 + 6i = 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 + 6i = 0 + -7

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

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

Divide each side by '6'.
i = -1.166666667

Simplifying
i = -1.166666667
Solution
i = {0, -2, -1.166666667}

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