(4X+12)(-6X+14)=0

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Solution for (4X+12)(-6X+14)=0 equation: 


Simplifying
(4X + 12)(-6X + 14) = 0

Reorder the terms:
(12 + 4X)(-6X + 14) = 0

Reorder the terms:
(12 + 4X)(14 + -6X) = 0

Multiply (12 + 4X) * (14 + -6X)
(12(14 + -6X) + 4X * (14 + -6X)) = 0
((14 * 12 + -6X * 12) + 4X * (14 + -6X)) = 0
((168 + -72X) + 4X * (14 + -6X)) = 0
(168 + -72X + (14 * 4X + -6X * 4X)) = 0
(168 + -72X + (56X + -24X2)) = 0

Combine like terms: -72X + 56X = -16X
(168 + -16X + -24X2) = 0

Solving
168 + -16X + -24X2 = 0

Solving for variable 'X'.

Factor out the Greatest Common Factor (GCF), '8'.
8(21 + -2X + -3X2) = 0

Factor a trinomial.
8((7 + -3X)(3 + X)) = 0

Ignore the factor 8.

Subproblem 1
Set the factor '(7 + -3X)' equal to zero and attempt to solve:

Simplifying
7 + -3X = 0

Solving
7 + -3X = 0

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

Add '-7' to each side of the equation.
7 + -7 + -3X = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -3X = 0 + -7
-3X = 0 + -7

Combine like terms: 0 + -7 = -7
-3X = -7

Divide each side by '-3'.
X = 2.333333333

Simplifying
X = 2.333333333

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

Simplifying
3 + X = 0

Solving
3 + X = 0

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

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

Combine like terms: 3 + -3 = 0
0 + X = 0 + -3
X = 0 + -3

Combine like terms: 0 + -3 = -3
X = -3

Simplifying
X = -3
Solution
X = {2.333333333, -3}

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