(3x-1)(5x+20)=0

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Solution for (3x-1)(5x+20)=0 equation: 


Simplifying
(3x + -1)(5x + 20) = 0

Reorder the terms:
(-1 + 3x)(5x + 20) = 0

Reorder the terms:
(-1 + 3x)(20 + 5x) = 0

Multiply (-1 + 3x) * (20 + 5x)
(-1(20 + 5x) + 3x * (20 + 5x)) = 0
((20 * -1 + 5x * -1) + 3x * (20 + 5x)) = 0
((-20 + -5x) + 3x * (20 + 5x)) = 0
(-20 + -5x + (20 * 3x + 5x * 3x)) = 0
(-20 + -5x + (60x + 15x2)) = 0

Combine like terms: -5x + 60x = 55x
(-20 + 55x + 15x2) = 0

Solving
-20 + 55x + 15x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-4 + 11x + 3x2) = 0

Factor a trinomial.
5((-4 + -1x)(1 + -3x)) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-4 + -1x)' equal to zero and attempt to solve:

Simplifying
-4 + -1x = 0

Solving
-4 + -1x = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1x = 0 + 4
-1x = 0 + 4

Combine like terms: 0 + 4 = 4
-1x = 4

Divide each side by '-1'.
x = -4

Simplifying
x = -4

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 = {-4, 0.3333333333}

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