(2x+14)(3x+12)=0

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Solution for (2x+14)(3x+12)=0 equation: 


Simplifying
(2x + 14)(3x + 12) = 0

Reorder the terms:
(14 + 2x)(3x + 12) = 0

Reorder the terms:
(14 + 2x)(12 + 3x) = 0

Multiply (14 + 2x) * (12 + 3x)
(14(12 + 3x) + 2x * (12 + 3x)) = 0
((12 * 14 + 3x * 14) + 2x * (12 + 3x)) = 0
((168 + 42x) + 2x * (12 + 3x)) = 0
(168 + 42x + (12 * 2x + 3x * 2x)) = 0
(168 + 42x + (24x + 6x2)) = 0

Combine like terms: 42x + 24x = 66x
(168 + 66x + 6x2) = 0

Solving
168 + 66x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6'.
6(28 + 11x + x2) = 0

Factor a trinomial.
6((7 + x)(4 + x)) = 0

Ignore the factor 6.

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

Simplifying
7 + x = 0

Solving
7 + x = 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 + x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + x = 0 + -7
x = 0 + -7

Combine like terms: 0 + -7 = -7
x = -7

Simplifying
x = -7

Subproblem 2
Set the factor '(4 + x)' equal to zero and attempt to solve:

Simplifying
4 + x = 0

Solving
4 + x = 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 + x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + x = 0 + -4
x = 0 + -4

Combine like terms: 0 + -4 = -4
x = -4

Simplifying
x = -4
Solution
x = {-7, -4}

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