(3x+12)(12x-23)=

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Solution for (3x+12)(12x-23)= equation: 


Simplifying
(3x + 12)(12x + -23) = 0

Reorder the terms:
(12 + 3x)(12x + -23) = 0

Reorder the terms:
(12 + 3x)(-23 + 12x) = 0

Multiply (12 + 3x) * (-23 + 12x)
(12(-23 + 12x) + 3x * (-23 + 12x)) = 0
((-23 * 12 + 12x * 12) + 3x * (-23 + 12x)) = 0
((-276 + 144x) + 3x * (-23 + 12x)) = 0
(-276 + 144x + (-23 * 3x + 12x * 3x)) = 0
(-276 + 144x + (-69x + 36x2)) = 0

Combine like terms: 144x + -69x = 75x
(-276 + 75x + 36x2) = 0

Solving
-276 + 75x + 36x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-92 + 25x + 12x2) = 0

Factor a trinomial.
3((-4 + -1x)(23 + -12x)) = 0

Ignore the factor 3.

Subproblem 1
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

Subproblem 2
Set the factor '(23 + -12x)' equal to zero and attempt to solve:

Simplifying
23 + -12x = 0

Solving
23 + -12x = 0

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

Add '-23' to each side of the equation.
23 + -23 + -12x = 0 + -23

Combine like terms: 23 + -23 = 0
0 + -12x = 0 + -23
-12x = 0 + -23

Combine like terms: 0 + -23 = -23
-12x = -23

Divide each side by '-12'.
x = 1.916666667

Simplifying
x = 1.916666667
Solution
x = {-4, 1.916666667}

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