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

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


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

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

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

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

Combine like terms: 9x + -2x = 7x
(-3 + 7x + 6x2) = 2

Solving
-3 + 7x + 6x2 = 2

Solving for variable 'x'.

Reorder the terms:
-3 + -2 + 7x + 6x2 = 2 + -2

Combine like terms: -3 + -2 = -5
-5 + 7x + 6x2 = 2 + -2

Combine like terms: 2 + -2 = 0
-5 + 7x + 6x2 = 0

Factor a trinomial.
(-5 + -3x)(1 + -2x) = 0

Subproblem 1

Set the factor '(-5 + -3x)' equal to zero and attempt to solve: Simplifying -5 + -3x = 0 Solving -5 + -3x = 0 Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -3x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -3x = 0 + 5 -3x = 0 + 5 Combine like terms: 0 + 5 = 5 -3x = 5 Divide each side by '-3'. x = -1.666666667 Simplifying x = -1.666666667

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 = {-1.666666667, 0.5}

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