5=-2x^2+6x+1

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

Simplifying
5 = -2x2 + 6x + 1

Reorder the terms:
5 = 1 + 6x + -2x2

Solving
5 = 1 + 6x + -2x2

Solving for variable 'x'.

Combine like terms: 5 + -1 = 4
4 + -6x + 2x2 = 1 + 6x + -2x2 + -1 + -6x + 2x2

Reorder the terms:
4 + -6x + 2x2 = 1 + -1 + 6x + -6x + -2x2 + 2x2

Combine like terms: 1 + -1 = 0
4 + -6x + 2x2 = 0 + 6x + -6x + -2x2 + 2x2
4 + -6x + 2x2 = 6x + -6x + -2x2 + 2x2

Combine like terms: 6x + -6x = 0
4 + -6x + 2x2 = 0 + -2x2 + 2x2
4 + -6x + 2x2 = -2x2 + 2x2

Combine like terms: -2x2 + 2x2 = 0
4 + -6x + 2x2 = 0

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

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

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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {1, 2}