120=2x^2+3x+1

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Solution for 120=2x^2+3x+1 equation: 


Simplifying
120 = 2x2 + 3x + 1

Reorder the terms:
120 = 1 + 3x + 2x2

Solving
120 = 1 + 3x + 2x2

Solving for variable 'x'.

Combine like terms: 120 + -1 = 119
119 + -3x + -2x2 = 1 + 3x + 2x2 + -1 + -3x + -2x2

Reorder the terms:
119 + -3x + -2x2 = 1 + -1 + 3x + -3x + 2x2 + -2x2

Combine like terms: 1 + -1 = 0
119 + -3x + -2x2 = 0 + 3x + -3x + 2x2 + -2x2
119 + -3x + -2x2 = 3x + -3x + 2x2 + -2x2

Combine like terms: 3x + -3x = 0
119 + -3x + -2x2 = 0 + 2x2 + -2x2
119 + -3x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
119 + -3x + -2x2 = 0

Factor a trinomial.
(7 + -1x)(17 + 2x) = 0


Subproblem 1
Set the factor '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7

Subproblem 2
Set the factor '(17 + 2x)' equal to zero and attempt to solve:

Simplifying
17 + 2x = 0

Solving
17 + 2x = 0

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

Add '-17' to each side of the equation.
17 + -17 + 2x = 0 + -17

Combine like terms: 17 + -17 = 0
0 + 2x = 0 + -17
2x = 0 + -17

Combine like terms: 0 + -17 = -17
2x = -17

Divide each side by '2'.
x = -8.5

Simplifying
x = -8.5
Solution
x = {7, -8.5}

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