9x^2+61x+52=0

Solution for 9x^2+61x+52=0 equation:

Simplifying
9x2 + 61x + 52 = 0

Reorder the terms:
52 + 61x + 9x2 = 0

Solving
52 + 61x + 9x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(52 + 9x)(1 + x) = 0

Subproblem 1
Set the factor '(52 + 9x)' equal to zero and attempt to solve:

Simplifying
52 + 9x = 0

Solving
52 + 9x = 0

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

Add '-52' to each side of the equation.
52 + -52 + 9x = 0 + -52

Combine like terms: 52 + -52 = 0
0 + 9x = 0 + -52
9x = 0 + -52

Combine like terms: 0 + -52 = -52
9x = -52

Divide each side by '9'.
x = -5.777777778

Simplifying
x = -5.777777778
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 = {-5.777777778, -1}