3(X+2)(X-5)=0

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Solution for 3(X+2)(X-5)=0 equation: 


Simplifying
3(X + 2)(X + -5) = 0

Reorder the terms:
3(2 + X)(X + -5) = 0

Reorder the terms:
3(2 + X)(-5 + X) = 0

Multiply (2 + X) * (-5 + X)
3(2(-5 + X) + X(-5 + X)) = 0
3((-5 * 2 + X * 2) + X(-5 + X)) = 0
3((-10 + 2X) + X(-5 + X)) = 0
3(-10 + 2X + (-5 * X + X * X)) = 0
3(-10 + 2X + (-5X + X2)) = 0

Combine like terms: 2X + -5X = -3X
3(-10 + -3X + X2) = 0
(-10 * 3 + -3X * 3 + X2 * 3) = 0
(-30 + -9X + 3X2) = 0

Solving
-30 + -9X + 3X2 = 0

Solving for variable 'X'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-10 + -3X + X2) = 0

Factor a trinomial.
3((-2 + -1X)(5 + -1X)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-2 + -1X)' equal to zero and attempt to solve:

Simplifying
-2 + -1X = 0

Solving
-2 + -1X = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1X = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1X = 0 + 2
-1X = 0 + 2

Combine like terms: 0 + 2 = 2
-1X = 2

Divide each side by '-1'.
X = -2

Simplifying
X = -2

Subproblem 2
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
Solution
X = {-2, 5}

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