(3x+9)(6x+7)=0

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Solution for (3x+9)(6x+7)=0 equation:


Simplifying
(3x + 9)(6x + 7) = 0

Reorder the terms:
(9 + 3x)(6x + 7) = 0

Reorder the terms:
(9 + 3x)(7 + 6x) = 0

Multiply (9 + 3x) * (7 + 6x)
(9(7 + 6x) + 3x * (7 + 6x)) = 0
((7 * 9 + 6x * 9) + 3x * (7 + 6x)) = 0
((63 + 54x) + 3x * (7 + 6x)) = 0
(63 + 54x + (7 * 3x + 6x * 3x)) = 0
(63 + 54x + (21x + 18x2)) = 0

Combine like terms: 54x + 21x = 75x
(63 + 75x + 18x2) = 0

Solving
63 + 75x + 18x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(21 + 25x + 6x2) = 0

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

Ignore the factor 3.

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 '(7 + 6x)' equal to zero and attempt to solve: Simplifying 7 + 6x = 0 Solving 7 + 6x = 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 + 6x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 6x = 0 + -7 6x = 0 + -7 Combine like terms: 0 + -7 = -7 6x = -7 Divide each side by '6'. x = -1.166666667 Simplifying x = -1.166666667

Solution

x = {-3, -1.166666667}

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