3x^2+42x+105=0

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Solution for 3x^2+42x+105=0 equation: 


Simplifying
3x2 + 42x + 105 = 0

Reorder the terms:
105 + 42x + 3x2 = 0

Solving
105 + 42x + 3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(35 + 14x + x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(35 + 14x + x2)' equal to zero and attempt to solve:

Simplifying
35 + 14x + x2 = 0

Solving
35 + 14x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-35' to each side of the equation.
35 + 14x + -35 + x2 = 0 + -35

Reorder the terms:
35 + -35 + 14x + x2 = 0 + -35

Combine like terms: 35 + -35 = 0
0 + 14x + x2 = 0 + -35
14x + x2 = 0 + -35

Combine like terms: 0 + -35 = -35
14x + x2 = -35

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 = -35 + 49

Reorder the terms:
49 + 14x + x2 = -35 + 49

Combine like terms: -35 + 49 = 14
49 + 14x + x2 = 14

Factor a perfect square on the left side:
(x + 7)(x + 7) = 14

Calculate the square root of the right side: 3.741657387

Break this problem into two subproblems by setting 
(x + 7) equal to 3.741657387 and -3.741657387.


Subproblem 1
x + 7 = 3.741657387

Simplifying
x + 7 = 3.741657387

Reorder the terms:
7 + x = 3.741657387

Solving
7 + x = 3.741657387

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 = 3.741657387 + -7

Combine like terms: 7 + -7 = 0
0 + x = 3.741657387 + -7
x = 3.741657387 + -7

Combine like terms: 3.741657387 + -7 = -3.258342613
x = -3.258342613

Simplifying
x = -3.258342613


Subproblem 2
x + 7 = -3.741657387

Simplifying
x + 7 = -3.741657387

Reorder the terms:
7 + x = -3.741657387

Solving
7 + x = -3.741657387

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 = -3.741657387 + -7

Combine like terms: 7 + -7 = 0
0 + x = -3.741657387 + -7
x = -3.741657387 + -7

Combine like terms: -3.741657387 + -7 = -10.741657387
x = -10.741657387

Simplifying
x = -10.741657387


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-3.258342613, -10.741657387}
Solution
x = {-3.258342613, -10.741657387}

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