9x^2=53x+6

Solution for 9x^2=53x+6 equation:

Simplifying
9x2 = 53x + 6

Reorder the terms:
9x2 = 6 + 53x

Solving
9x2 = 6 + 53x

Solving for variable 'x'.

Reorder the terms:
-6 + -53x + 9x2 = 6 + 53x + -6 + -53x

Reorder the terms:
-6 + -53x + 9x2 = 6 + -6 + 53x + -53x

Combine like terms: 6 + -6 = 0
-6 + -53x + 9x2 = 0 + 53x + -53x
-6 + -53x + 9x2 = 53x + -53x

Combine like terms: 53x + -53x = 0
-6 + -53x + 9x2 = 0

Factor a trinomial.
(-1 + -9x)(6 + -1x) = 0

Subproblem 1
Set the factor '(-1 + -9x)' equal to zero and attempt to solve:

Simplifying
-1 + -9x = 0

Solving
-1 + -9x = 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 + -9x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -9x = 0 + 1
-9x = 0 + 1

Combine like terms: 0 + 1 = 1
-9x = 1

Divide each side by '-9'.
x = -0.1111111111

Simplifying
x = -0.1111111111
Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

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

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

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {-0.1111111111, 6}