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

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


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

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

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

Multiply (-2 + 3x) * (3 + x)
(-2(3 + x) + 3x * (3 + x)) = 20
((3 * -2 + x * -2) + 3x * (3 + x)) = 20
((-6 + -2x) + 3x * (3 + x)) = 20
(-6 + -2x + (3 * 3x + x * 3x)) = 20
(-6 + -2x + (9x + 3x2)) = 20

Combine like terms: -2x + 9x = 7x
(-6 + 7x + 3x2) = 20

Solving
-6 + 7x + 3x2 = 20

Solving for variable 'x'.

Reorder the terms:
-6 + -20 + 7x + 3x2 = 20 + -20

Combine like terms: -6 + -20 = -26
-26 + 7x + 3x2 = 20 + -20

Combine like terms: 20 + -20 = 0
-26 + 7x + 3x2 = 0

Factor a trinomial.
(-13 + -3x)(2 + -1x) = 0


Subproblem 1
Set the factor '(-13 + -3x)' equal to zero and attempt to solve:

Simplifying
-13 + -3x = 0

Solving
-13 + -3x = 0

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

Add '13' to each side of the equation.
-13 + 13 + -3x = 0 + 13

Combine like terms: -13 + 13 = 0
0 + -3x = 0 + 13
-3x = 0 + 13

Combine like terms: 0 + 13 = 13
-3x = 13

Divide each side by '-3'.
x = -4.333333333

Simplifying
x = -4.333333333

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 = {-4.333333333, 2}

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