9x^2+12x+4=-30x-41

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Solution for 9x^2+12x+4=-30x-41 equation: 


Simplifying
9x2 + 12x + 4 = -30x + -41

Reorder the terms:
4 + 12x + 9x2 = -30x + -41

Reorder the terms:
4 + 12x + 9x2 = -41 + -30x

Solving
4 + 12x + 9x2 = -41 + -30x

Solving for variable 'x'.

Reorder the terms:
4 + 41 + 12x + 30x + 9x2 = -41 + -30x + 41 + 30x

Combine like terms: 4 + 41 = 45
45 + 12x + 30x + 9x2 = -41 + -30x + 41 + 30x

Combine like terms: 12x + 30x = 42x
45 + 42x + 9x2 = -41 + -30x + 41 + 30x

Reorder the terms:
45 + 42x + 9x2 = -41 + 41 + -30x + 30x

Combine like terms: -41 + 41 = 0
45 + 42x + 9x2 = 0 + -30x + 30x
45 + 42x + 9x2 = -30x + 30x

Combine like terms: -30x + 30x = 0
45 + 42x + 9x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(15 + 14x + 3x2) = 0

Factor a trinomial.
3((3 + x)(5 + 3x)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 0

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

Add '-3' to each side of the equation.
3 + -3 + x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + x = 0 + -3
x = 0 + -3

Combine like terms: 0 + -3 = -3
x = -3

Simplifying
x = -3

Subproblem 2
Set the factor '(5 + 3x)' equal to zero and attempt to solve:

Simplifying
5 + 3x = 0

Solving
5 + 3x = 0

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

Add '-5' to each side of the equation.
5 + -5 + 3x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 3x = 0 + -5
3x = 0 + -5

Combine like terms: 0 + -5 = -5
3x = -5

Divide each side by '3'.
x = -1.666666667

Simplifying
x = -1.666666667
Solution
x = {-3, -1.666666667}

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