(4+2i)x(7+5i)=

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Solution for (4+2i)x(7+5i)= equation: 


Simplifying
(4 + 2i) * x(7 + 5i) = 0

Reorder the terms for easier multiplication:
x(4 + 2i)(7 + 5i) = 0

Multiply (4 + 2i) * (7 + 5i)
x(4(7 + 5i) + 2i * (7 + 5i)) = 0
x((7 * 4 + 5i * 4) + 2i * (7 + 5i)) = 0
x((28 + 20i) + 2i * (7 + 5i)) = 0
x(28 + 20i + (7 * 2i + 5i * 2i)) = 0
x(28 + 20i + (14i + 10i2)) = 0

Combine like terms: 20i + 14i = 34i
x(28 + 34i + 10i2) = 0
(28 * x + 34i * x + 10i2 * x) = 0

Reorder the terms:
(34ix + 10i2x + 28x) = 0
(34ix + 10i2x + 28x) = 0

Solving
34ix + 10i2x + 28x = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(17i + 5i2 + 14) = 0

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

Ignore the factor 2.

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

Simplifying
x = 0

Solving
x = 0

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

Add '-1x' to each side of the equation.
x + -1x = 0 + -1x
Remove the zero:
0 = -1x

Simplifying
0 = -1x

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 2
Set the factor '(5i + 7)' equal to zero and attempt to solve:

Simplifying
5i + 7 = 0

Reorder the terms:
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 '(i + 2)' equal to zero and attempt to solve:

Simplifying
i + 2 = 0

Reorder the terms:
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
Solution
i = {-1.4, -2}

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