(3x+1)(2x+3)=3

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Solution for (3x+1)(2x+3)=3 equation:


Simplifying
(3x + 1)(2x + 3) = 3

Reorder the terms:
(1 + 3x)(2x + 3) = 3

Reorder the terms:
(1 + 3x)(3 + 2x) = 3

Multiply (1 + 3x) * (3 + 2x)
(1(3 + 2x) + 3x * (3 + 2x)) = 3
((3 * 1 + 2x * 1) + 3x * (3 + 2x)) = 3
((3 + 2x) + 3x * (3 + 2x)) = 3
(3 + 2x + (3 * 3x + 2x * 3x)) = 3
(3 + 2x + (9x + 6x2)) = 3

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

Add '-3' to each side of the equation.
3 + 11x + -3 + 6x2 = 3 + -3

Reorder the terms:
3 + -3 + 11x + 6x2 = 3 + -3

Combine like terms: 3 + -3 = 0
0 + 11x + 6x2 = 3 + -3
11x + 6x2 = 3 + -3

Combine like terms: 3 + -3 = 0
11x + 6x2 = 0

Solving
11x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(11 + 6x) = 0

Subproblem 1

Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0

Subproblem 2

Set the factor '(11 + 6x)' equal to zero and attempt to solve: Simplifying 11 + 6x = 0 Solving 11 + 6x = 0 Move all terms containing x to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + 6x = 0 + -11 Combine like terms: 11 + -11 = 0 0 + 6x = 0 + -11 6x = 0 + -11 Combine like terms: 0 + -11 = -11 6x = -11 Divide each side by '6'. x = -1.833333333 Simplifying x = -1.833333333

Solution

x = {0, -1.833333333}

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