9x^2+62x+61=6x^2+41x+31

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Solution for 9x^2+62x+61=6x^2+41x+31 equation: 


Simplifying
9x2 + 62x + 61 = 6x2 + 41x + 31

Reorder the terms:
61 + 62x + 9x2 = 6x2 + 41x + 31

Reorder the terms:
61 + 62x + 9x2 = 31 + 41x + 6x2

Solving
61 + 62x + 9x2 = 31 + 41x + 6x2

Solving for variable 'x'.

Reorder the terms:
61 + -31 + 62x + -41x + 9x2 + -6x2 = 31 + 41x + 6x2 + -31 + -41x + -6x2

Combine like terms: 61 + -31 = 30
30 + 62x + -41x + 9x2 + -6x2 = 31 + 41x + 6x2 + -31 + -41x + -6x2

Combine like terms: 62x + -41x = 21x
30 + 21x + 9x2 + -6x2 = 31 + 41x + 6x2 + -31 + -41x + -6x2

Combine like terms: 9x2 + -6x2 = 3x2
30 + 21x + 3x2 = 31 + 41x + 6x2 + -31 + -41x + -6x2

Reorder the terms:
30 + 21x + 3x2 = 31 + -31 + 41x + -41x + 6x2 + -6x2

Combine like terms: 31 + -31 = 0
30 + 21x + 3x2 = 0 + 41x + -41x + 6x2 + -6x2
30 + 21x + 3x2 = 41x + -41x + 6x2 + -6x2

Combine like terms: 41x + -41x = 0
30 + 21x + 3x2 = 0 + 6x2 + -6x2
30 + 21x + 3x2 = 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
30 + 21x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(10 + 7x + x2) = 0

Factor a trinomial.
3((5 + x)(2 + x)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(5 + x)' equal to zero and attempt to solve:

Simplifying
5 + x = 0

Solving
5 + x = 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 + x = 0 + -5

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

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

Simplifying
x = -5

Subproblem 2
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
Solution
x = {-5, -2}

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