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

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


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

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

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

Multiply (2 + 3x) * (-3 + 2x)
(2(-3 + 2x) + 3x * (-3 + 2x)) = 0
((-3 * 2 + 2x * 2) + 3x * (-3 + 2x)) = 0
((-6 + 4x) + 3x * (-3 + 2x)) = 0
(-6 + 4x + (-3 * 3x + 2x * 3x)) = 0
(-6 + 4x + (-9x + 6x2)) = 0

Combine like terms: 4x + -9x = -5x
(-6 + -5x + 6x2) = 0

Solving
-6 + -5x + 6x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-2 + -3x)(3 + -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 '(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

Solution

x = {-0.6666666667, 1.5}

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