0=5x^2+6x+1

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Solution for 0=5x^2+6x+1 equation: 


Simplifying
0 = 5x2 + 6x + 1

Reorder the terms:
0 = 1 + 6x + 5x2

Solving
0 = 1 + 6x + 5x2

Solving for variable 'x'.

Combine like terms: 0 + -1 = -1
-1 + -6x + -5x2 = 1 + 6x + 5x2 + -1 + -6x + -5x2

Reorder the terms:
-1 + -6x + -5x2 = 1 + -1 + 6x + -6x + 5x2 + -5x2

Combine like terms: 1 + -1 = 0
-1 + -6x + -5x2 = 0 + 6x + -6x + 5x2 + -5x2
-1 + -6x + -5x2 = 6x + -6x + 5x2 + -5x2

Combine like terms: 6x + -6x = 0
-1 + -6x + -5x2 = 0 + 5x2 + -5x2
-1 + -6x + -5x2 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
-1 + -6x + -5x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(1 + 6x + 5x2) = 0

Factor a trinomial.
-1((1 + x)(1 + 5x)) = 0

Ignore the factor -1.

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

Simplifying
1 + x = 0

Solving
1 + x = 0

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

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

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

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

Simplifying
x = -1

Subproblem 2
Set the factor '(1 + 5x)' equal to zero and attempt to solve:

Simplifying
1 + 5x = 0

Solving
1 + 5x = 0

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

Add '-1' to each side of the equation.
1 + -1 + 5x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 5x = 0 + -1
5x = 0 + -1

Combine like terms: 0 + -1 = -1
5x = -1

Divide each side by '5'.
x = -0.2

Simplifying
x = -0.2
Solution
x = {-1, -0.2}

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