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

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


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

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

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

Multiply (2 + 3x) * (3 + x)
(2(3 + x) + 3x * (3 + x)) = 0
((3 * 2 + x * 2) + 3x * (3 + x)) = 0
((6 + 2x) + 3x * (3 + x)) = 0
(6 + 2x + (3 * 3x + x * 3x)) = 0
(6 + 2x + (9x + 3x2)) = 0

Combine like terms: 2x + 9x = 11x
(6 + 11x + 3x2) = 0

Solving
6 + 11x + 3x2 = 0

Solving for variable 'x'.

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

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 '(2 + 3x)' equal to zero and attempt to solve: Simplifying 2 + 3x = 0 Solving 2 + 3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + 3x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 3x = 0 + -2 3x = 0 + -2 Combine like terms: 0 + -2 = -2 3x = -2 Divide each side by '3'. x = -0.6666666667 Simplifying x = -0.6666666667

Solution

x = {-3, -0.6666666667}

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