(3x-12)(x+5)=0

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Solution for (3x-12)(x+5)=0 equation: 


Simplifying
(3x + -12)(x + 5) = 0

Reorder the terms:
(-12 + 3x)(x + 5) = 0

Reorder the terms:
(-12 + 3x)(5 + x) = 0

Multiply (-12 + 3x) * (5 + x)
(-12(5 + x) + 3x * (5 + x)) = 0
((5 * -12 + x * -12) + 3x * (5 + x)) = 0
((-60 + -12x) + 3x * (5 + x)) = 0
(-60 + -12x + (5 * 3x + x * 3x)) = 0
(-60 + -12x + (15x + 3x2)) = 0

Combine like terms: -12x + 15x = 3x
(-60 + 3x + 3x2) = 0

Solving
-60 + 3x + 3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-20 + x + x2) = 0

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

Ignore the factor 3.

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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