(3x+9)(14-2x)=0

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Solution for (3x+9)(14-2x)=0 equation: 


Simplifying
(3x + 9)(14 + -2x) = 0

Reorder the terms:
(9 + 3x)(14 + -2x) = 0

Multiply (9 + 3x) * (14 + -2x)
(9(14 + -2x) + 3x * (14 + -2x)) = 0
((14 * 9 + -2x * 9) + 3x * (14 + -2x)) = 0
((126 + -18x) + 3x * (14 + -2x)) = 0
(126 + -18x + (14 * 3x + -2x * 3x)) = 0
(126 + -18x + (42x + -6x2)) = 0

Combine like terms: -18x + 42x = 24x
(126 + 24x + -6x2) = 0

Solving
126 + 24x + -6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6'.
6(21 + 4x + -1x2) = 0

Factor a trinomial.
6((7 + -1x)(3 + x)) = 0

Ignore the factor 6.

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

Simplifying
7 + -1x = 0

Solving
7 + -1x = 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 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7

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 = {7, -3}

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