(3x+9)(4x+6)=

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Solution for (3x+9)(4x+6)= equation:


Simplifying
(3x + 9)(4x + 6) = 0

Reorder the terms:
(9 + 3x)(4x + 6) = 0

Reorder the terms:
(9 + 3x)(6 + 4x) = 0

Multiply (9 + 3x) * (6 + 4x)
(9(6 + 4x) + 3x * (6 + 4x)) = 0
((6 * 9 + 4x * 9) + 3x * (6 + 4x)) = 0
((54 + 36x) + 3x * (6 + 4x)) = 0
(54 + 36x + (6 * 3x + 4x * 3x)) = 0
(54 + 36x + (18x + 12x2)) = 0

Combine like terms: 36x + 18x = 54x
(54 + 54x + 12x2) = 0

Solving
54 + 54x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6'.
6(9 + 9x + 2x2) = 0

Factor a trinomial.
6((3 + x)(3 + 2x)) = 0

Ignore the factor 6.

Subproblem 1

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

Subproblem 2

Set the factor '(3 + 2x)' equal to zero and attempt to solve: Simplifying 3 + 2x = 0 Solving 3 + 2x = 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 + 2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2x = 0 + -3 2x = 0 + -3 Combine like terms: 0 + -3 = -3 2x = -3 Divide each side by '2'. x = -1.5 Simplifying x = -1.5

Solution

x = {-3, -1.5}

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