3j^2-30j+12=0

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Solution for 3j^2-30j+12=0 equation: 


Simplifying
3j2 + -30j + 12 = 0

Reorder the terms:
12 + -30j + 3j2 = 0

Solving
12 + -30j + 3j2 = 0

Solving for variable 'j'.

Factor out the Greatest Common Factor (GCF), '3'.
3(4 + -10j + j2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(4 + -10j + j2)' equal to zero and attempt to solve:

Simplifying
4 + -10j + j2 = 0

Solving
4 + -10j + j2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + -10j + -4 + j2 = 0 + -4

Reorder the terms:
4 + -4 + -10j + j2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -10j + j2 = 0 + -4
-10j + j2 = 0 + -4

Combine like terms: 0 + -4 = -4
-10j + j2 = -4

The j term is -10j.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10j + 25 + j2 = -4 + 25

Reorder the terms:
25 + -10j + j2 = -4 + 25

Combine like terms: -4 + 25 = 21
25 + -10j + j2 = 21

Factor a perfect square on the left side:
(j + -5)(j + -5) = 21

Calculate the square root of the right side: 4.582575695

Break this problem into two subproblems by setting 
(j + -5) equal to 4.582575695 and -4.582575695.


Subproblem 1
j + -5 = 4.582575695

Simplifying
j + -5 = 4.582575695

Reorder the terms:
-5 + j = 4.582575695

Solving
-5 + j = 4.582575695

Solving for variable 'j'.

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 = 4.582575695 + 5

Combine like terms: -5 + 5 = 0
0 + j = 4.582575695 + 5
j = 4.582575695 + 5

Combine like terms: 4.582575695 + 5 = 9.582575695
j = 9.582575695

Simplifying
j = 9.582575695


Subproblem 2
j + -5 = -4.582575695

Simplifying
j + -5 = -4.582575695

Reorder the terms:
-5 + j = -4.582575695

Solving
-5 + j = -4.582575695

Solving for variable 'j'.

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 = -4.582575695 + 5

Combine like terms: -5 + 5 = 0
0 + j = -4.582575695 + 5
j = -4.582575695 + 5

Combine like terms: -4.582575695 + 5 = 0.417424305
j = 0.417424305

Simplifying
j = 0.417424305


Solution
The solution to the problem is based on the solutions
from the subproblems.
j = {9.582575695, 0.417424305}
Solution
j = {9.582575695, 0.417424305}

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