(3x-1)(x+2)=20

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Solution for (3x-1)(x+2)=20 equation: 


Simplifying
(3x + -1)(x + 2) = 20

Reorder the terms:
(-1 + 3x)(x + 2) = 20

Reorder the terms:
(-1 + 3x)(2 + x) = 20

Multiply (-1 + 3x) * (2 + x)
(-1(2 + x) + 3x * (2 + x)) = 20
((2 * -1 + x * -1) + 3x * (2 + x)) = 20
((-2 + -1x) + 3x * (2 + x)) = 20
(-2 + -1x + (2 * 3x + x * 3x)) = 20
(-2 + -1x + (6x + 3x2)) = 20

Combine like terms: -1x + 6x = 5x
(-2 + 5x + 3x2) = 20

Solving
-2 + 5x + 3x2 = 20

Solving for variable 'x'.

Reorder the terms:
-2 + -20 + 5x + 3x2 = 20 + -20

Combine like terms: -2 + -20 = -22
-22 + 5x + 3x2 = 20 + -20

Combine like terms: 20 + -20 = 0
-22 + 5x + 3x2 = 0

Factor a trinomial.
(-11 + -3x)(2 + -1x) = 0


Subproblem 1
Set the factor '(-11 + -3x)' equal to zero and attempt to solve:

Simplifying
-11 + -3x = 0

Solving
-11 + -3x = 0

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

Add '11' to each side of the equation.
-11 + 11 + -3x = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -3x = 0 + 11
-3x = 0 + 11

Combine like terms: 0 + 11 = 11
-3x = 11

Divide each side by '-3'.
x = -3.666666667

Simplifying
x = -3.666666667

Subproblem 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 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 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-3.666666667, 2}

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