3x^2+1=6x-2

Solution for 3x^2+1=6x-2 equation:

Simplifying
3x2 + 1 = 6x + -2

Reorder the terms:
1 + 3x2 = 6x + -2

Reorder the terms:
1 + 3x2 = -2 + 6x

Solving
1 + 3x2 = -2 + 6x

Solving for variable 'x'.

Reorder the terms:
1 + 2 + -6x + 3x2 = -2 + 6x + 2 + -6x

Combine like terms: 1 + 2 = 3
3 + -6x + 3x2 = -2 + 6x + 2 + -6x

Reorder the terms:
3 + -6x + 3x2 = -2 + 2 + 6x + -6x

Combine like terms: -2 + 2 = 0
3 + -6x + 3x2 = 0 + 6x + -6x
3 + -6x + 3x2 = 6x + -6x

Combine like terms: 6x + -6x = 0
3 + -6x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(1 + -2x + x2) = 0

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

Ignore the factor 3.
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 '(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 = {1, 1}