(2x+3)(2x+1)=0

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Solution for (2x+3)(2x+1)=0 equation:


Simplifying
(2x + 3)(2x + 1) = 0

Reorder the terms:
(3 + 2x)(2x + 1) = 0

Reorder the terms:
(3 + 2x)(1 + 2x) = 0

Multiply (3 + 2x) * (1 + 2x)
(3(1 + 2x) + 2x * (1 + 2x)) = 0
((1 * 3 + 2x * 3) + 2x * (1 + 2x)) = 0
((3 + 6x) + 2x * (1 + 2x)) = 0
(3 + 6x + (1 * 2x + 2x * 2x)) = 0
(3 + 6x + (2x + 4x2)) = 0

Combine like terms: 6x + 2x = 8x
(3 + 8x + 4x2) = 0

Solving
3 + 8x + 4x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(3 + 2x)(1 + 2x) = 0

Subproblem 1

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

Subproblem 2

Set the factor '(1 + 2x)' equal to zero and attempt to solve: Simplifying 1 + 2x = 0 Solving 1 + 2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2x = 0 + -1 2x = 0 + -1 Combine like terms: 0 + -1 = -1 2x = -1 Divide each side by '2'. x = -0.5 Simplifying x = -0.5

Solution

x = {-1.5, -0.5}

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