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

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


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

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

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

Combine like terms: -3x + 4x = 1x
(2 + 1x + -6x2) = 0

Solving
2 + 1x + -6x2 = 0

Solving for variable 'x'.

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

Subproblem 1

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

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 = {0.6666666667, -0.5}

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