5(s+i)(2s+4i)=0

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Solution for 5(s+i)(2s+4i)=0 equation: 


Simplifying
5(s + i)(2s + 4i) = 0

Reorder the terms:
5(i + s)(2s + 4i) = 0

Reorder the terms:
5(i + s)(4i + 2s) = 0

Multiply (i + s) * (4i + 2s)
5(i(4i + 2s) + s(4i + 2s)) = 0
5((4i * i + 2s * i) + s(4i + 2s)) = 0

Reorder the terms:
5((2is + 4i2) + s(4i + 2s)) = 0
5((2is + 4i2) + s(4i + 2s)) = 0
5(2is + 4i2 + (4i * s + 2s * s)) = 0
5(2is + 4i2 + (4is + 2s2)) = 0

Reorder the terms:
5(2is + 4is + 4i2 + 2s2) = 0

Combine like terms: 2is + 4is = 6is
5(6is + 4i2 + 2s2) = 0
(6is * 5 + 4i2 * 5 + 2s2 * 5) = 0
(30is + 20i2 + 10s2) = 0

Solving
30is + 20i2 + 10s2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '10'.
10(3is + 2i2 + s2) = 0

Factor a trinomial.
10((2i + s)(i + s)) = 0

Ignore the factor 10.

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

Simplifying
2i + s = 0

Solving
2i + s = 0

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

Add '-1s' to each side of the equation.
2i + s + -1s = 0 + -1s

Combine like terms: s + -1s = 0
2i + 0 = 0 + -1s
2i = 0 + -1s
Remove the zero:
2i = -1s

Divide each side by '2'.
i = -0.5s

Simplifying
i = -0.5s

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

Simplifying
i + s = 0

Solving
i + s = 0

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

Add '-1s' to each side of the equation.
i + s + -1s = 0 + -1s

Combine like terms: s + -1s = 0
i + 0 = 0 + -1s
i = 0 + -1s
Remove the zero:
i = -1s

Simplifying
i = -1s
Solution
i = {-0.5s, -1s}

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