x^2+20x=-2x^2+10x+5200

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Solution for x^2+20x=-2x^2+10x+5200 equation: 


Simplifying
x2 + 20x = -2x2 + 10x + 5200

Reorder the terms:
20x + x2 = -2x2 + 10x + 5200

Reorder the terms:
20x + x2 = 5200 + 10x + -2x2

Solving
20x + x2 = 5200 + 10x + -2x2

Solving for variable 'x'.

Reorder the terms:
-5200 + 20x + -10x + x2 + 2x2 = 5200 + 10x + -2x2 + -5200 + -10x + 2x2

Combine like terms: 20x + -10x = 10x
-5200 + 10x + x2 + 2x2 = 5200 + 10x + -2x2 + -5200 + -10x + 2x2

Combine like terms: x2 + 2x2 = 3x2
-5200 + 10x + 3x2 = 5200 + 10x + -2x2 + -5200 + -10x + 2x2

Reorder the terms:
-5200 + 10x + 3x2 = 5200 + -5200 + 10x + -10x + -2x2 + 2x2

Combine like terms: 5200 + -5200 = 0
-5200 + 10x + 3x2 = 0 + 10x + -10x + -2x2 + 2x2
-5200 + 10x + 3x2 = 10x + -10x + -2x2 + 2x2

Combine like terms: 10x + -10x = 0
-5200 + 10x + 3x2 = 0 + -2x2 + 2x2
-5200 + 10x + 3x2 = -2x2 + 2x2

Combine like terms: -2x2 + 2x2 = 0
-5200 + 10x + 3x2 = 0

Factor a trinomial.
(-130 + -3x)(40 + -1x) = 0


Subproblem 1
Set the factor '(-130 + -3x)' equal to zero and attempt to solve:

Simplifying
-130 + -3x = 0

Solving
-130 + -3x = 0

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

Add '130' to each side of the equation.
-130 + 130 + -3x = 0 + 130

Combine like terms: -130 + 130 = 0
0 + -3x = 0 + 130
-3x = 0 + 130

Combine like terms: 0 + 130 = 130
-3x = 130

Divide each side by '-3'.
x = -43.33333333

Simplifying
x = -43.33333333

Subproblem 2
Set the factor '(40 + -1x)' equal to zero and attempt to solve:

Simplifying
40 + -1x = 0

Solving
40 + -1x = 0

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

Add '-40' to each side of the equation.
40 + -40 + -1x = 0 + -40

Combine like terms: 40 + -40 = 0
0 + -1x = 0 + -40
-1x = 0 + -40

Combine like terms: 0 + -40 = -40
-1x = -40

Divide each side by '-1'.
x = 40

Simplifying
x = 40
Solution
x = {-43.33333333, 40}

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