0=9x^2+29x+22

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Solution for 0=9x^2+29x+22 equation: 


Simplifying
0 = 9x2 + 29x + 22

Reorder the terms:
0 = 22 + 29x + 9x2

Solving
0 = 22 + 29x + 9x2

Solving for variable 'x'.

Combine like terms: 0 + -22 = -22
-22 + -29x + -9x2 = 22 + 29x + 9x2 + -22 + -29x + -9x2

Reorder the terms:
-22 + -29x + -9x2 = 22 + -22 + 29x + -29x + 9x2 + -9x2

Combine like terms: 22 + -22 = 0
-22 + -29x + -9x2 = 0 + 29x + -29x + 9x2 + -9x2
-22 + -29x + -9x2 = 29x + -29x + 9x2 + -9x2

Combine like terms: 29x + -29x = 0
-22 + -29x + -9x2 = 0 + 9x2 + -9x2
-22 + -29x + -9x2 = 9x2 + -9x2

Combine like terms: 9x2 + -9x2 = 0
-22 + -29x + -9x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(22 + 29x + 9x2) = 0

Factor a trinomial.
-1((2 + x)(11 + 9x)) = 0

Ignore the factor -1.

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

Simplifying
2 + x = 0

Solving
2 + x = 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 + x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + x = 0 + -2
x = 0 + -2

Combine like terms: 0 + -2 = -2
x = -2

Simplifying
x = -2

Subproblem 2
Set the factor '(11 + 9x)' equal to zero and attempt to solve:

Simplifying
11 + 9x = 0

Solving
11 + 9x = 0

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

Add '-11' to each side of the equation.
11 + -11 + 9x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + 9x = 0 + -11
9x = 0 + -11

Combine like terms: 0 + -11 = -11
9x = -11

Divide each side by '9'.
x = -1.222222222

Simplifying
x = -1.222222222
Solution
x = {-2, -1.222222222}

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