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

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


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

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

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

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

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

Add '6' to each side of the equation.
-6 + 7x + 6 + 3x2 = -6 + 6

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

Combine like terms: -6 + 6 = 0
0 + 7x + 3x2 = -6 + 6
7x + 3x2 = -6 + 6

Combine like terms: -6 + 6 = 0
7x + 3x2 = 0

Solving
7x + 3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(7 + 3x) = 0


Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

Move all terms containing x to the left, all other terms to the right.

Simplifying
x = 0

Subproblem 2
Set the factor '(7 + 3x)' equal to zero and attempt to solve:

Simplifying
7 + 3x = 0

Solving
7 + 3x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-7' to each side of the equation.
7 + -7 + 3x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 3x = 0 + -7
3x = 0 + -7

Combine like terms: 0 + -7 = -7
3x = -7

Divide each side by '3'.
x = -2.333333333

Simplifying
x = -2.333333333
Solution
x = {0, -2.333333333}

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