-3x(x+2)-8(x+2)=0

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Solution for -3x(x+2)-8(x+2)=0 equation: 


Simplifying
-3x(x + 2) + -8(x + 2) = 0

Reorder the terms:
-3x(2 + x) + -8(x + 2) = 0
(2 * -3x + x * -3x) + -8(x + 2) = 0
(-6x + -3x2) + -8(x + 2) = 0

Reorder the terms:
-6x + -3x2 + -8(2 + x) = 0
-6x + -3x2 + (2 * -8 + x * -8) = 0
-6x + -3x2 + (-16 + -8x) = 0

Reorder the terms:
-16 + -6x + -8x + -3x2 = 0

Combine like terms: -6x + -8x = -14x
-16 + -14x + -3x2 = 0

Solving
-16 + -14x + -3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(16 + 14x + 3x2) = 0

Factor a trinomial.
-1((8 + 3x)(2 + x)) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(8 + 3x)' equal to zero and attempt to solve:

Simplifying
8 + 3x = 0

Solving
8 + 3x = 0

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

Add '-8' to each side of the equation.
8 + -8 + 3x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + 3x = 0 + -8
3x = 0 + -8

Combine like terms: 0 + -8 = -8
3x = -8

Divide each side by '3'.
x = -2.666666667

Simplifying
x = -2.666666667

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

Simplifying
2 + x = 0

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

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

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

Simplifying
x = -2
Solution
x = {-2.666666667, -2}

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