2x^2+10x+1=13

Solution for 2x^2+10x+1=13 equation:

Simplifying
2x2 + 10x + 1 = 13

Reorder the terms:
1 + 10x + 2x2 = 13

Solving
1 + 10x + 2x2 = 13

Solving for variable 'x'.

Reorder the terms:
1 + -13 + 10x + 2x2 = 13 + -13

Combine like terms: 1 + -13 = -12
-12 + 10x + 2x2 = 13 + -13

Combine like terms: 13 + -13 = 0
-12 + 10x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-6 + 5x + x2) = 0

Factor a trinomial.
2((-6 + -1x)(1 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-6 + -1x)' equal to zero and attempt to solve:

Simplifying
-6 + -1x = 0

Solving
-6 + -1x = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1x = 0 + 6

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

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

Divide each side by '-1'.
x = -6

Simplifying
x = -6
Subproblem 2
Set the factor '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 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 + -1x = 0 + -1

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

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

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

Simplifying
x = 1
Solution
x = {-6, 1}