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

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


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

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

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

Multiply (1 + 2x) * (-2 + 3x)
(1(-2 + 3x) + 2x * (-2 + 3x)) = 20
((-2 * 1 + 3x * 1) + 2x * (-2 + 3x)) = 20
((-2 + 3x) + 2x * (-2 + 3x)) = 20
(-2 + 3x + (-2 * 2x + 3x * 2x)) = 20
(-2 + 3x + (-4x + 6x2)) = 20

Combine like terms: 3x + -4x = -1x
(-2 + -1x + 6x2) = 20

Solving
-2 + -1x + 6x2 = 20

Solving for variable 'x'.

Reorder the terms:
-2 + -20 + -1x + 6x2 = 20 + -20

Combine like terms: -2 + -20 = -22
-22 + -1x + 6x2 = 20 + -20

Combine like terms: 20 + -20 = 0
-22 + -1x + 6x2 = 0

Factor a trinomial.
(-11 + -6x)(2 + -1x) = 0


Subproblem 1
Set the factor '(-11 + -6x)' equal to zero and attempt to solve:

Simplifying
-11 + -6x = 0

Solving
-11 + -6x = 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 + -6x = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -6x = 0 + 11
-6x = 0 + 11

Combine like terms: 0 + 11 = 11
-6x = 11

Divide each side by '-6'.
x = -1.833333333

Simplifying
x = -1.833333333

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 = {-1.833333333, 2}

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