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

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


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

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

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

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

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

Solving
0 = -2 + -1x + 6x2

Solving for variable 'x'.

Combine like terms: 0 + 2 = 2
2 + x + -6x2 = -2 + -1x + 6x2 + 2 + x + -6x2

Reorder the terms:
2 + x + -6x2 = -2 + 2 + -1x + x + 6x2 + -6x2

Combine like terms: -2 + 2 = 0
2 + x + -6x2 = 0 + -1x + x + 6x2 + -6x2
2 + x + -6x2 = -1x + x + 6x2 + -6x2

Combine like terms: -1x + x = 0
2 + x + -6x2 = 0 + 6x2 + -6x2
2 + x + -6x2 = 6x2 + -6x2

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

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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