2j^2+2j=j^2-15-6j

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Solution for 2j^2+2j=j^2-15-6j equation:


Simplifying
2j2 + 2j = j2 + -15 + -6j

Reorder the terms:
2j + 2j2 = j2 + -15 + -6j

Reorder the terms:
2j + 2j2 = -15 + -6j + j2

Solving
2j + 2j2 = -15 + -6j + j2

Solving for variable 'j'.

Reorder the terms:
15 + 2j + 6j + 2j2 + -1j2 = -15 + -6j + j2 + 15 + 6j + -1j2

Combine like terms: 2j + 6j = 8j
15 + 8j + 2j2 + -1j2 = -15 + -6j + j2 + 15 + 6j + -1j2

Combine like terms: 2j2 + -1j2 = 1j2
15 + 8j + 1j2 = -15 + -6j + j2 + 15 + 6j + -1j2

Reorder the terms:
15 + 8j + 1j2 = -15 + 15 + -6j + 6j + j2 + -1j2

Combine like terms: -15 + 15 = 0
15 + 8j + 1j2 = 0 + -6j + 6j + j2 + -1j2
15 + 8j + 1j2 = -6j + 6j + j2 + -1j2

Combine like terms: -6j + 6j = 0
15 + 8j + 1j2 = 0 + j2 + -1j2
15 + 8j + 1j2 = j2 + -1j2

Combine like terms: j2 + -1j2 = 0
15 + 8j + 1j2 = 0

Factor a trinomial.
(5 + j)(3 + j) = 0


Subproblem 1
Set the factor '(5 + j)' equal to zero and attempt to solve:

Simplifying
5 + j = 0

Solving
5 + j = 0

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

Add '-5' to each side of the equation.
5 + -5 + j = 0 + -5

Combine like terms: 5 + -5 = 0
0 + j = 0 + -5
j = 0 + -5

Combine like terms: 0 + -5 = -5
j = -5

Simplifying
j = -5

Subproblem 2
Set the factor '(3 + j)' equal to zero and attempt to solve:

Simplifying
3 + j = 0

Solving
3 + j = 0

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

Add '-3' to each side of the equation.
3 + -3 + j = 0 + -3

Combine like terms: 3 + -3 = 0
0 + j = 0 + -3
j = 0 + -3

Combine like terms: 0 + -3 = -3
j = -3

Simplifying
j = -3
Solution
j = {-5, -3}

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