x^2+30x=-2x^2+10x+3300

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Solution for x^2+30x=-2x^2+10x+3300 equation: 


Simplifying
x2 + 30x = -2x2 + 10x + 3300

Reorder the terms:
30x + x2 = -2x2 + 10x + 3300

Reorder the terms:
30x + x2 = 3300 + 10x + -2x2

Solving
30x + x2 = 3300 + 10x + -2x2

Solving for variable 'x'.

Reorder the terms:
-3300 + 30x + -10x + x2 + 2x2 = 3300 + 10x + -2x2 + -3300 + -10x + 2x2

Combine like terms: 30x + -10x = 20x
-3300 + 20x + x2 + 2x2 = 3300 + 10x + -2x2 + -3300 + -10x + 2x2

Combine like terms: x2 + 2x2 = 3x2
-3300 + 20x + 3x2 = 3300 + 10x + -2x2 + -3300 + -10x + 2x2

Reorder the terms:
-3300 + 20x + 3x2 = 3300 + -3300 + 10x + -10x + -2x2 + 2x2

Combine like terms: 3300 + -3300 = 0
-3300 + 20x + 3x2 = 0 + 10x + -10x + -2x2 + 2x2
-3300 + 20x + 3x2 = 10x + -10x + -2x2 + 2x2

Combine like terms: 10x + -10x = 0
-3300 + 20x + 3x2 = 0 + -2x2 + 2x2
-3300 + 20x + 3x2 = -2x2 + 2x2

Combine like terms: -2x2 + 2x2 = 0
-3300 + 20x + 3x2 = 0

Factor a trinomial.
(-110 + -3x)(30 + -1x) = 0


Subproblem 1
Set the factor '(-110 + -3x)' equal to zero and attempt to solve:

Simplifying
-110 + -3x = 0

Solving
-110 + -3x = 0

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

Add '110' to each side of the equation.
-110 + 110 + -3x = 0 + 110

Combine like terms: -110 + 110 = 0
0 + -3x = 0 + 110
-3x = 0 + 110

Combine like terms: 0 + 110 = 110
-3x = 110

Divide each side by '-3'.
x = -36.66666667

Simplifying
x = -36.66666667

Subproblem 2
Set the factor '(30 + -1x)' equal to zero and attempt to solve:

Simplifying
30 + -1x = 0

Solving
30 + -1x = 0

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

Add '-30' to each side of the equation.
30 + -30 + -1x = 0 + -30

Combine like terms: 30 + -30 = 0
0 + -1x = 0 + -30
-1x = 0 + -30

Combine like terms: 0 + -30 = -30
-1x = -30

Divide each side by '-1'.
x = 30

Simplifying
x = 30
Solution
x = {-36.66666667, 30}

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