3x^2-42x+30=0

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Solution for 3x^2-42x+30=0 equation: 


Simplifying
3x2 + -42x + 30 = 0

Reorder the terms:
30 + -42x + 3x2 = 0

Solving
30 + -42x + 3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(10 + -14x + x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(10 + -14x + x2)' equal to zero and attempt to solve:

Simplifying
10 + -14x + x2 = 0

Solving
10 + -14x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-10' to each side of the equation.
10 + -14x + -10 + x2 = 0 + -10

Reorder the terms:
10 + -10 + -14x + x2 = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -14x + x2 = 0 + -10
-14x + x2 = 0 + -10

Combine like terms: 0 + -10 = -10
-14x + x2 = -10

The x term is -14x.  Take half its coefficient (-7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
-14x + 49 + x2 = -10 + 49

Reorder the terms:
49 + -14x + x2 = -10 + 49

Combine like terms: -10 + 49 = 39
49 + -14x + x2 = 39

Factor a perfect square on the left side:
(x + -7)(x + -7) = 39

Calculate the square root of the right side: 6.244997998

Break this problem into two subproblems by setting 
(x + -7) equal to 6.244997998 and -6.244997998.


Subproblem 1
x + -7 = 6.244997998

Simplifying
x + -7 = 6.244997998

Reorder the terms:
-7 + x = 6.244997998

Solving
-7 + x = 6.244997998

Solving for variable 'x'.

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

Add '7' to each side of the equation.
-7 + 7 + x = 6.244997998 + 7

Combine like terms: -7 + 7 = 0
0 + x = 6.244997998 + 7
x = 6.244997998 + 7

Combine like terms: 6.244997998 + 7 = 13.244997998
x = 13.244997998

Simplifying
x = 13.244997998


Subproblem 2
x + -7 = -6.244997998

Simplifying
x + -7 = -6.244997998

Reorder the terms:
-7 + x = -6.244997998

Solving
-7 + x = -6.244997998

Solving for variable 'x'.

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

Add '7' to each side of the equation.
-7 + 7 + x = -6.244997998 + 7

Combine like terms: -7 + 7 = 0
0 + x = -6.244997998 + 7
x = -6.244997998 + 7

Combine like terms: -6.244997998 + 7 = 0.755002002
x = 0.755002002

Simplifying
x = 0.755002002


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {13.244997998, 0.755002002}
Solution
x = {13.244997998, 0.755002002}

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