0=9x^2+62x+53

Solution for 0=9x^2+62x+53 equation:

Simplifying
0 = 9x2 + 62x + 53

Reorder the terms:
0 = 53 + 62x + 9x2

Solving
0 = 53 + 62x + 9x2

Solving for variable 'x'.

Combine like terms: 0 + -53 = -53
-53 + -62x + -9x2 = 53 + 62x + 9x2 + -53 + -62x + -9x2

Reorder the terms:
-53 + -62x + -9x2 = 53 + -53 + 62x + -62x + 9x2 + -9x2

Combine like terms: 53 + -53 = 0
-53 + -62x + -9x2 = 0 + 62x + -62x + 9x2 + -9x2
-53 + -62x + -9x2 = 62x + -62x + 9x2 + -9x2

Combine like terms: 62x + -62x = 0
-53 + -62x + -9x2 = 0 + 9x2 + -9x2
-53 + -62x + -9x2 = 9x2 + -9x2

Combine like terms: 9x2 + -9x2 = 0
-53 + -62x + -9x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(53 + 62x + 9x2) = 0

Factor a trinomial.
-1((53 + 9x)(1 + x)) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(53 + 9x)' equal to zero and attempt to solve:

Simplifying
53 + 9x = 0

Solving
53 + 9x = 0

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

Add '-53' to each side of the equation.
53 + -53 + 9x = 0 + -53

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

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

Divide each side by '9'.
x = -5.888888889

Simplifying
x = -5.888888889
Subproblem 2
Set the factor '(1 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

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

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

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

Simplifying
x = -1
Solution
x = {-5.888888889, -1}