(x-4)(5x-15)=0

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Solution for (x-4)(5x-15)=0 equation: 


Simplifying
(x + -4)(5x + -15) = 0

Reorder the terms:
(-4 + x)(5x + -15) = 0

Reorder the terms:
(-4 + x)(-15 + 5x) = 0

Multiply (-4 + x) * (-15 + 5x)
(-4(-15 + 5x) + x(-15 + 5x)) = 0
((-15 * -4 + 5x * -4) + x(-15 + 5x)) = 0
((60 + -20x) + x(-15 + 5x)) = 0
(60 + -20x + (-15 * x + 5x * x)) = 0
(60 + -20x + (-15x + 5x2)) = 0

Combine like terms: -20x + -15x = -35x
(60 + -35x + 5x2) = 0

Solving
60 + -35x + 5x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(12 + -7x + x2) = 0

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

Ignore the factor 5.

Subproblem 1
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

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 = {3, 4}

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