2x^2-6x+3=11

Solution for 2x^2-6x+3=11 equation:

Simplifying
2x2 + -6x + 3 = 11

Reorder the terms:
3 + -6x + 2x2 = 11

Solving
3 + -6x + 2x2 = 11

Solving for variable 'x'.

Reorder the terms:
3 + -11 + -6x + 2x2 = 11 + -11

Combine like terms: 3 + -11 = -8
-8 + -6x + 2x2 = 11 + -11

Combine like terms: 11 + -11 = 0
-8 + -6x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-4 + -3x + x2) = 0

Factor a trinomial.
2((-1 + -1x)(4 + -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 '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {-1, 4}