2x^2+2x+1=61

Solution for 2x^2+2x+1=61 equation:

Simplifying
2x2 + 2x + 1 = 61

Reorder the terms:
1 + 2x + 2x2 = 61

Solving
1 + 2x + 2x2 = 61

Solving for variable 'x'.

Reorder the terms:
1 + -61 + 2x + 2x2 = 61 + -61

Combine like terms: 1 + -61 = -60
-60 + 2x + 2x2 = 61 + -61

Combine like terms: 61 + -61 = 0
-60 + 2x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-30 + x + x2) = 0

Factor a trinomial.
2((-6 + -1x)(5 + -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 '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

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

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

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

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {-6, 5}