(3x+15)(5x-20)=0

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Solution for (3x+15)(5x-20)=0 equation: 


Simplifying
(3x + 15)(5x + -20) = 0

Reorder the terms:
(15 + 3x)(5x + -20) = 0

Reorder the terms:
(15 + 3x)(-20 + 5x) = 0

Multiply (15 + 3x) * (-20 + 5x)
(15(-20 + 5x) + 3x * (-20 + 5x)) = 0
((-20 * 15 + 5x * 15) + 3x * (-20 + 5x)) = 0
((-300 + 75x) + 3x * (-20 + 5x)) = 0
(-300 + 75x + (-20 * 3x + 5x * 3x)) = 0
(-300 + 75x + (-60x + 15x2)) = 0

Combine like terms: 75x + -60x = 15x
(-300 + 15x + 15x2) = 0

Solving
-300 + 15x + 15x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '15'.
15(-20 + x + x2) = 0

Factor a trinomial.
15((-5 + -1x)(4 + -1x)) = 0

Ignore the factor 15.

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 '(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 = {-5, 4}

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