6x-2=3x^2+1

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

Simplifying
6x + -2 = 3x2 + 1

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

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

Solving
-2 + 6x = 1 + 3x2

Solving for variable 'x'.

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

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

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

Combine like terms: 1 + -1 = 0
-3 + 6x + -3x2 = 0 + 3x2 + -3x2
-3 + 6x + -3x2 = 3x2 + -3x2

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

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

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

Ignore the factor 3.
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 + -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}