x^2+9x+30=60-2x^2

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Solution for x^2+9x+30=60-2x^2 equation: 


Simplifying
x2 + 9x + 30 = 60 + -2x2

Reorder the terms:
30 + 9x + x2 = 60 + -2x2

Solving
30 + 9x + x2 = 60 + -2x2

Solving for variable 'x'.

Reorder the terms:
30 + -60 + 9x + x2 + 2x2 = 60 + -2x2 + -60 + 2x2

Combine like terms: 30 + -60 = -30
-30 + 9x + x2 + 2x2 = 60 + -2x2 + -60 + 2x2

Combine like terms: x2 + 2x2 = 3x2
-30 + 9x + 3x2 = 60 + -2x2 + -60 + 2x2

Reorder the terms:
-30 + 9x + 3x2 = 60 + -60 + -2x2 + 2x2

Combine like terms: 60 + -60 = 0
-30 + 9x + 3x2 = 0 + -2x2 + 2x2
-30 + 9x + 3x2 = -2x2 + 2x2

Combine like terms: -2x2 + 2x2 = 0
-30 + 9x + 3x2 = 0

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

Factor a trinomial.
3((-5 + -1x)(2 + -1x)) = 0

Ignore the factor 3.

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

Simplifying
-5 + -1x = 0

Solving
-5 + -1x = 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 + -1x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1x = 0 + 5
-1x = 0 + 5

Combine like terms: 0 + 5 = 5
-1x = 5

Divide each side by '-1'.
x = -5

Simplifying
x = -5

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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 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 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

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

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