(12x-4)(3x+16)=0

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Solution for (12x-4)(3x+16)=0 equation: 


Simplifying
(12x + -4)(3x + 16) = 0

Reorder the terms:
(-4 + 12x)(3x + 16) = 0

Reorder the terms:
(-4 + 12x)(16 + 3x) = 0

Multiply (-4 + 12x) * (16 + 3x)
(-4(16 + 3x) + 12x * (16 + 3x)) = 0
((16 * -4 + 3x * -4) + 12x * (16 + 3x)) = 0
((-64 + -12x) + 12x * (16 + 3x)) = 0
(-64 + -12x + (16 * 12x + 3x * 12x)) = 0
(-64 + -12x + (192x + 36x2)) = 0

Combine like terms: -12x + 192x = 180x
(-64 + 180x + 36x2) = 0

Solving
-64 + 180x + 36x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-16 + 45x + 9x2) = 0

Factor a trinomial.
4((-16 + -3x)(1 + -3x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-16 + -3x)' equal to zero and attempt to solve:

Simplifying
-16 + -3x = 0

Solving
-16 + -3x = 0

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

Add '16' to each side of the equation.
-16 + 16 + -3x = 0 + 16

Combine like terms: -16 + 16 = 0
0 + -3x = 0 + 16
-3x = 0 + 16

Combine like terms: 0 + 16 = 16
-3x = 16

Divide each side by '-3'.
x = -5.333333333

Simplifying
x = -5.333333333

Subproblem 2
Set the factor '(1 + -3x)' equal to zero and attempt to solve:

Simplifying
1 + -3x = 0

Solving
1 + -3x = 0

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

Add '-1' to each side of the equation.
1 + -1 + -3x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3x = 0 + -1
-3x = 0 + -1

Combine like terms: 0 + -1 = -1
-3x = -1

Divide each side by '-3'.
x = 0.3333333333

Simplifying
x = 0.3333333333
Solution
x = {-5.333333333, 0.3333333333}

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