204=6x^2+10x+4

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Solution for 204=6x^2+10x+4 equation: 


Simplifying
204 = 6x2 + 10x + 4

Reorder the terms:
204 = 4 + 10x + 6x2

Solving
204 = 4 + 10x + 6x2

Solving for variable 'x'.

Combine like terms: 204 + -4 = 200
200 + -10x + -6x2 = 4 + 10x + 6x2 + -4 + -10x + -6x2

Reorder the terms:
200 + -10x + -6x2 = 4 + -4 + 10x + -10x + 6x2 + -6x2

Combine like terms: 4 + -4 = 0
200 + -10x + -6x2 = 0 + 10x + -10x + 6x2 + -6x2
200 + -10x + -6x2 = 10x + -10x + 6x2 + -6x2

Combine like terms: 10x + -10x = 0
200 + -10x + -6x2 = 0 + 6x2 + -6x2
200 + -10x + -6x2 = 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
200 + -10x + -6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(100 + -5x + -3x2) = 0

Factor a trinomial.
2((5 + -1x)(20 + 3x)) = 0

Ignore the factor 2.

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 '(20 + 3x)' equal to zero and attempt to solve:

Simplifying
20 + 3x = 0

Solving
20 + 3x = 0

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

Add '-20' to each side of the equation.
20 + -20 + 3x = 0 + -20

Combine like terms: 20 + -20 = 0
0 + 3x = 0 + -20
3x = 0 + -20

Combine like terms: 0 + -20 = -20
3x = -20

Divide each side by '3'.
x = -6.666666667

Simplifying
x = -6.666666667
Solution
x = {5, -6.666666667}

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