(3x+6)(2x-1)=

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Solution for (3x+6)(2x-1)= equation: 


Simplifying
(3x + 6)(2x + -1) = 0

Reorder the terms:
(6 + 3x)(2x + -1) = 0

Reorder the terms:
(6 + 3x)(-1 + 2x) = 0

Multiply (6 + 3x) * (-1 + 2x)
(6(-1 + 2x) + 3x * (-1 + 2x)) = 0
((-1 * 6 + 2x * 6) + 3x * (-1 + 2x)) = 0
((-6 + 12x) + 3x * (-1 + 2x)) = 0
(-6 + 12x + (-1 * 3x + 2x * 3x)) = 0
(-6 + 12x + (-3x + 6x2)) = 0

Combine like terms: 12x + -3x = 9x
(-6 + 9x + 6x2) = 0

Solving
-6 + 9x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-2 + 3x + 2x2) = 0

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

Ignore the factor 3.

Subproblem 1
Set the factor '(-2 + -1x)' equal to zero and attempt to solve:

Simplifying
-2 + -1x = 0

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

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

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

Divide each side by '-1'.
x = -2

Simplifying
x = -2

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 = {-2, 0.5}

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