(3x-5)(x+2)=20

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Solution for (3x-5)(x+2)=20 equation: 


Simplifying
(3x + -5)(x + 2) = 20

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

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

Multiply (-5 + 3x) * (2 + x)
(-5(2 + x) + 3x * (2 + x)) = 20
((2 * -5 + x * -5) + 3x * (2 + x)) = 20
((-10 + -5x) + 3x * (2 + x)) = 20
(-10 + -5x + (2 * 3x + x * 3x)) = 20
(-10 + -5x + (6x + 3x2)) = 20

Combine like terms: -5x + 6x = 1x
(-10 + 1x + 3x2) = 20

Solving
-10 + 1x + 3x2 = 20

Solving for variable 'x'.

Reorder the terms:
-10 + -20 + 1x + 3x2 = 20 + -20

Combine like terms: -10 + -20 = -30
-30 + 1x + 3x2 = 20 + -20

Combine like terms: 20 + -20 = 0
-30 + 1x + 3x2 = 0

Factor a trinomial.
(-10 + -3x)(3 + -1x) = 0


Subproblem 1
Set the factor '(-10 + -3x)' equal to zero and attempt to solve:

Simplifying
-10 + -3x = 0

Solving
-10 + -3x = 0

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

Add '10' to each side of the equation.
-10 + 10 + -3x = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -3x = 0 + 10
-3x = 0 + 10

Combine like terms: 0 + 10 = 10
-3x = 10

Divide each side by '-3'.
x = -3.333333333

Simplifying
x = -3.333333333

Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-3.333333333, 3}

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