(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 = -65x
(20 + -65x + 15x2) = 0

Solving
20 + -65x + 15x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(4 + -13x + 3x2) = 0

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

Ignore the factor 5.

Subproblem 1
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

Subproblem 2
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
Solution
x = {0.3333333333, 4}

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