13x^2-13x+9=x^2+6

Solution for 13x^2-13x+9=x^2+6 equation:

Simplifying
13x2 + -13x + 9 = x2 + 6

Reorder the terms:
9 + -13x + 13x2 = x2 + 6

Reorder the terms:
9 + -13x + 13x2 = 6 + x2

Solving
9 + -13x + 13x2 = 6 + x2

Solving for variable 'x'.

Reorder the terms:
9 + -6 + -13x + 13x2 + -1x2 = 6 + x2 + -6 + -1x2

Combine like terms: 9 + -6 = 3
3 + -13x + 13x2 + -1x2 = 6 + x2 + -6 + -1x2

Combine like terms: 13x2 + -1x2 = 12x2
3 + -13x + 12x2 = 6 + x2 + -6 + -1x2

Reorder the terms:
3 + -13x + 12x2 = 6 + -6 + x2 + -1x2

Combine like terms: 6 + -6 = 0
3 + -13x + 12x2 = 0 + x2 + -1x2
3 + -13x + 12x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
3 + -13x + 12x2 = 0

Factor a trinomial.
(1 + -3x)(3 + -4x) = 0

Subproblem 1
Set the factor '(1 + -3x)' equal to zero and attempt to solve:

Simplifying
1 + -3x = 0

Solving
1 + -3x = 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 + -3x = 0 + -1

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

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

Divide each side by '-3'.
x = 0.3333333333

Simplifying
x = 0.3333333333
Subproblem 2
Set the factor '(3 + -4x)' equal to zero and attempt to solve:

Simplifying
3 + -4x = 0

Solving
3 + -4x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -4x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -4x = 0 + -3
-4x = 0 + -3

Combine like terms: 0 + -3 = -3
-4x = -3

Divide each side by '-4'.
x = 0.75

Simplifying
x = 0.75
Solution
x = {0.3333333333, 0.75}