(9x+3)(20-4x)=0

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Solution for (9x+3)(20-4x)=0 equation: 


Simplifying
(9x + 3)(20 + -4x) = 0

Reorder the terms:
(3 + 9x)(20 + -4x) = 0

Multiply (3 + 9x) * (20 + -4x)
(3(20 + -4x) + 9x * (20 + -4x)) = 0
((20 * 3 + -4x * 3) + 9x * (20 + -4x)) = 0
((60 + -12x) + 9x * (20 + -4x)) = 0
(60 + -12x + (20 * 9x + -4x * 9x)) = 0
(60 + -12x + (180x + -36x2)) = 0

Combine like terms: -12x + 180x = 168x
(60 + 168x + -36x2) = 0

Solving
60 + 168x + -36x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '12'.
12(5 + 14x + -3x2) = 0

Factor a trinomial.
12((5 + -1x)(1 + 3x)) = 0

Ignore the factor 12.

Subproblem 1
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 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 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5

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

Simplifying
1 + 3x = 0

Solving
1 + 3x = 0

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

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

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

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

Divide each side by '3'.
x = -0.3333333333

Simplifying
x = -0.3333333333
Solution
x = {5, -0.3333333333}

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