9X^2-14X=X+6

Solution for 9X^2-14X=X+6 equation:

Simplifying
9X2 + -14X = X + 6

Reorder the terms:
-14X + 9X2 = X + 6

Reorder the terms:
-14X + 9X2 = 6 + X

Solving
-14X + 9X2 = 6 + X

Solving for variable 'X'.

Reorder the terms:
-6 + -14X + -1X + 9X2 = 6 + X + -6 + -1X

Combine like terms: -14X + -1X = -15X
-6 + -15X + 9X2 = 6 + X + -6 + -1X

Reorder the terms:
-6 + -15X + 9X2 = 6 + -6 + X + -1X

Combine like terms: 6 + -6 = 0
-6 + -15X + 9X2 = 0 + X + -1X
-6 + -15X + 9X2 = X + -1X

Combine like terms: X + -1X = 0
-6 + -15X + 9X2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-2 + -5X + 3X2) = 0

Factor a trinomial.
3((-1 + -3X)(2 + -1X)) = 0

Ignore the factor 3.
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 '(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 = {-0.3333333333, 2}