6x-(x^2-3)=11

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

Simplifying
6x + -1(x2 + -3) = 11

Reorder the terms:
6x + -1(-3 + x2) = 11
6x + (-3 * -1 + x2 * -1) = 11
6x + (3 + -1x2) = 11

Reorder the terms:
3 + 6x + -1x2 = 11

Solving
3 + 6x + -1x2 = 11

Solving for variable 'x'.

Reorder the terms:
3 + -11 + 6x + -1x2 = 11 + -11

Combine like terms: 3 + -11 = -8
-8 + 6x + -1x2 = 11 + -11

Combine like terms: 11 + -11 = 0
-8 + 6x + -1x2 = 0

Factor a trinomial.
(-4 + x)(2 + -1x) = 0

Subproblem 1
Set the factor '(-4 + x)' equal to zero and attempt to solve:

Simplifying
-4 + x = 0

Solving
-4 + x = 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 + x = 0 + 4

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

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

Simplifying
x = 4
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 = {4, 2}