6*x^2+2x+1=49

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Solution for 6*x^2+2x+1=49 equation: 


Simplifying
6x2 + 2x + 1 = 49

Reorder the terms:
1 + 2x + 6x2 = 49

Solving
1 + 2x + 6x2 = 49

Solving for variable 'x'.

Reorder the terms:
1 + -49 + 2x + 6x2 = 49 + -49

Combine like terms: 1 + -49 = -48
-48 + 2x + 6x2 = 49 + -49

Combine like terms: 49 + -49 = 0
-48 + 2x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-24 + x + 3x2) = 0

Factor a trinomial.
2((-3 + -1x)(8 + -3x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-3 + -1x)' equal to zero and attempt to solve:

Simplifying
-3 + -1x = 0

Solving
-3 + -1x = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1x = 0 + 3
-1x = 0 + 3

Combine like terms: 0 + 3 = 3
-1x = 3

Divide each side by '-1'.
x = -3

Simplifying
x = -3

Subproblem 2
Set the factor '(8 + -3x)' equal to zero and attempt to solve:

Simplifying
8 + -3x = 0

Solving
8 + -3x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -3x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -3x = 0 + -8
-3x = 0 + -8

Combine like terms: 0 + -8 = -8
-3x = -8

Divide each side by '-3'.
x = 2.666666667

Simplifying
x = 2.666666667
Solution
x = {-3, 2.666666667}

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