2x^2+9x=6x+20

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Solution for 2x^2+9x=6x+20 equation: 


Simplifying
2x2 + 9x = 6x + 20

Reorder the terms:
9x + 2x2 = 6x + 20

Reorder the terms:
9x + 2x2 = 20 + 6x

Solving
9x + 2x2 = 20 + 6x

Solving for variable 'x'.

Reorder the terms:
-20 + 9x + -6x + 2x2 = 20 + 6x + -20 + -6x

Combine like terms: 9x + -6x = 3x
-20 + 3x + 2x2 = 20 + 6x + -20 + -6x

Reorder the terms:
-20 + 3x + 2x2 = 20 + -20 + 6x + -6x

Combine like terms: 20 + -20 = 0
-20 + 3x + 2x2 = 0 + 6x + -6x
-20 + 3x + 2x2 = 6x + -6x

Combine like terms: 6x + -6x = 0
-20 + 3x + 2x2 = 0

Factor a trinomial.
(-4 + -1x)(5 + -2x) = 0


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

Simplifying
-4 + -1x = 0

Solving
-4 + -1x = 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 + -1x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1x = 0 + 4
-1x = 0 + 4

Combine like terms: 0 + 4 = 4
-1x = 4

Divide each side by '-1'.
x = -4

Simplifying
x = -4

Subproblem 2
Set the factor '(5 + -2x)' equal to zero and attempt to solve:

Simplifying
5 + -2x = 0

Solving
5 + -2x = 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 + -2x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2x = 0 + -5
-2x = 0 + -5

Combine like terms: 0 + -5 = -5
-2x = -5

Divide each side by '-2'.
x = 2.5

Simplifying
x = 2.5
Solution
x = {-4, 2.5}

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