(3x-15)(24x-1200)=0

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Solution for (3x-15)(24x-1200)=0 equation: 


Simplifying
(3x + -15)(24x + -1200) = 0

Reorder the terms:
(-15 + 3x)(24x + -1200) = 0

Reorder the terms:
(-15 + 3x)(-1200 + 24x) = 0

Multiply (-15 + 3x) * (-1200 + 24x)
(-15(-1200 + 24x) + 3x * (-1200 + 24x)) = 0
((-1200 * -15 + 24x * -15) + 3x * (-1200 + 24x)) = 0
((18000 + -360x) + 3x * (-1200 + 24x)) = 0
(18000 + -360x + (-1200 * 3x + 24x * 3x)) = 0
(18000 + -360x + (-3600x + 72x2)) = 0

Combine like terms: -360x + -3600x = -3960x
(18000 + -3960x + 72x2) = 0

Solving
18000 + -3960x + 72x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '72'.
72(250 + -55x + x2) = 0

Factor a trinomial.
72((5 + -1x)(50 + -1x)) = 0

Ignore the factor 72.

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 '(50 + -1x)' equal to zero and attempt to solve:

Simplifying
50 + -1x = 0

Solving
50 + -1x = 0

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

Add '-50' to each side of the equation.
50 + -50 + -1x = 0 + -50

Combine like terms: 50 + -50 = 0
0 + -1x = 0 + -50
-1x = 0 + -50

Combine like terms: 0 + -50 = -50
-1x = -50

Divide each side by '-1'.
x = 50

Simplifying
x = 50
Solution
x = {5, 50}

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