(3x+6)(6x-3)=0

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Solution for (3x+6)(6x-3)=0 equation: 


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

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

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

Multiply (6 + 3x) * (-3 + 6x)
(6(-3 + 6x) + 3x * (-3 + 6x)) = 0
((-3 * 6 + 6x * 6) + 3x * (-3 + 6x)) = 0
((-18 + 36x) + 3x * (-3 + 6x)) = 0
(-18 + 36x + (-3 * 3x + 6x * 3x)) = 0
(-18 + 36x + (-9x + 18x2)) = 0

Combine like terms: 36x + -9x = 27x
(-18 + 27x + 18x2) = 0

Solving
-18 + 27x + 18x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '9'.
9(-2 + 3x + 2x2) = 0

Factor a trinomial.
9((-2 + -1x)(1 + -2x)) = 0

Ignore the factor 9.

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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