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

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


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

Multiply (6 + -2i) * (7 + -5i)
i(6(7 + -5i) + -2i * (7 + -5i)) = 0
i((7 * 6 + -5i * 6) + -2i * (7 + -5i)) = 0
i((42 + -30i) + -2i * (7 + -5i)) = 0
i(42 + -30i + (7 * -2i + -5i * -2i)) = 0
i(42 + -30i + (-14i + 10i2)) = 0

Combine like terms: -30i + -14i = -44i
i(42 + -44i + 10i2) = 0
(42 * i + -44i * i + 10i2 * i) = 0
(42i + -44i2 + 10i3) = 0

Solving
42i + -44i2 + 10i3 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '2i'.
2i(21 + -22i + 5i2) = 0

Factor a trinomial.
2i((7 + -5i)(3 + -1i)) = 0

Ignore the factor 2.

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 '(7 + -5i)' equal to zero and attempt to solve:

Simplifying
7 + -5i = 0

Solving
7 + -5i = 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 + -5i = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -5i = 0 + -7
-5i = 0 + -7

Combine like terms: 0 + -7 = -7
-5i = -7

Divide each side by '-5'.
i = 1.4

Simplifying
i = 1.4

Subproblem 3
Set the factor '(3 + -1i)' equal to zero and attempt to solve:

Simplifying
3 + -1i = 0

Solving
3 + -1i = 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 + -1i = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1i = 0 + -3
-1i = 0 + -3

Combine like terms: 0 + -3 = -3
-1i = -3

Divide each side by '-1'.
i = 3

Simplifying
i = 3
Solution
i = {0, 1.4, 3}

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