(2x+9)(4x+12)=0

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Solution for (2x+9)(4x+12)=0 equation: 


Simplifying
(2x + 9)(4x + 12) = 0

Reorder the terms:
(9 + 2x)(4x + 12) = 0

Reorder the terms:
(9 + 2x)(12 + 4x) = 0

Multiply (9 + 2x) * (12 + 4x)
(9(12 + 4x) + 2x * (12 + 4x)) = 0
((12 * 9 + 4x * 9) + 2x * (12 + 4x)) = 0
((108 + 36x) + 2x * (12 + 4x)) = 0
(108 + 36x + (12 * 2x + 4x * 2x)) = 0
(108 + 36x + (24x + 8x2)) = 0

Combine like terms: 36x + 24x = 60x
(108 + 60x + 8x2) = 0

Solving
108 + 60x + 8x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(27 + 15x + 2x2) = 0

Factor a trinomial.
4((9 + 2x)(3 + x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(9 + 2x)' equal to zero and attempt to solve:

Simplifying
9 + 2x = 0

Solving
9 + 2x = 0

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

Add '-9' to each side of the equation.
9 + -9 + 2x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + 2x = 0 + -9
2x = 0 + -9

Combine like terms: 0 + -9 = -9
2x = -9

Divide each side by '2'.
x = -4.5

Simplifying
x = -4.5

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 = {-4.5, -3}

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