3x^2+x=20+12x

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Solution for 3x^2+x=20+12x equation: 


Simplifying
3x2 + x = 20 + 12x

Reorder the terms:
x + 3x2 = 20 + 12x

Solving
x + 3x2 = 20 + 12x

Solving for variable 'x'.

Reorder the terms:
-20 + x + -12x + 3x2 = 20 + 12x + -20 + -12x

Combine like terms: x + -12x = -11x
-20 + -11x + 3x2 = 20 + 12x + -20 + -12x

Reorder the terms:
-20 + -11x + 3x2 = 20 + -20 + 12x + -12x

Combine like terms: 20 + -20 = 0
-20 + -11x + 3x2 = 0 + 12x + -12x
-20 + -11x + 3x2 = 12x + -12x

Combine like terms: 12x + -12x = 0
-20 + -11x + 3x2 = 0

Factor a trinomial.
(-4 + -3x)(5 + -1x) = 0


Subproblem 1
Set the factor '(-4 + -3x)' equal to zero and attempt to solve:

Simplifying
-4 + -3x = 0

Solving
-4 + -3x = 0

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

Add '4' to each side of the equation.
-4 + 4 + -3x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -3x = 0 + 4
-3x = 0 + 4

Combine like terms: 0 + 4 = 4
-3x = 4

Divide each side by '-3'.
x = -1.333333333

Simplifying
x = -1.333333333

Subproblem 2
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
Solution
x = {-1.333333333, 5}

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