20x=6x^2-2x+20

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Solution for 20x=6x^2-2x+20 equation: 


Simplifying
20x = 6x2 + -2x + 20

Reorder the terms:
20x = 20 + -2x + 6x2

Solving
20x = 20 + -2x + 6x2

Solving for variable 'x'.

Reorder the terms:
-20 + 20x + 2x + -6x2 = 20 + -2x + 6x2 + -20 + 2x + -6x2

Combine like terms: 20x + 2x = 22x
-20 + 22x + -6x2 = 20 + -2x + 6x2 + -20 + 2x + -6x2

Reorder the terms:
-20 + 22x + -6x2 = 20 + -20 + -2x + 2x + 6x2 + -6x2

Combine like terms: 20 + -20 = 0
-20 + 22x + -6x2 = 0 + -2x + 2x + 6x2 + -6x2
-20 + 22x + -6x2 = -2x + 2x + 6x2 + -6x2

Combine like terms: -2x + 2x = 0
-20 + 22x + -6x2 = 0 + 6x2 + -6x2
-20 + 22x + -6x2 = 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
-20 + 22x + -6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-10 + 11x + -3x2) = 0

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

Ignore the factor 2.

Subproblem 1
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

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 = {2, 1.666666667}

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