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

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Solution for 4(x+3)(-x-8)=0 equation: 


Simplifying
4(x + 3)(-1x + -8) = 0

Reorder the terms:
4(3 + x)(-1x + -8) = 0

Reorder the terms:
4(3 + x)(-8 + -1x) = 0

Multiply (3 + x) * (-8 + -1x)
4(3(-8 + -1x) + x(-8 + -1x)) = 0
4((-8 * 3 + -1x * 3) + x(-8 + -1x)) = 0
4((-24 + -3x) + x(-8 + -1x)) = 0
4(-24 + -3x + (-8 * x + -1x * x)) = 0
4(-24 + -3x + (-8x + -1x2)) = 0

Combine like terms: -3x + -8x = -11x
4(-24 + -11x + -1x2) = 0
(-24 * 4 + -11x * 4 + -1x2 * 4) = 0
(-96 + -44x + -4x2) = 0

Solving
-96 + -44x + -4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '-4'.
-4(24 + 11x + x2) = 0

Factor a trinomial.
-4((8 + x)(3 + x)) = 0

Ignore the factor -4.

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

Simplifying
8 + x = 0

Solving
8 + x = 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 + x = 0 + -8

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

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

Simplifying
x = -8

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

Simplifying
3 + x = 0

Solving
3 + x = 0

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

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

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

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

Simplifying
x = -3
Solution
x = {-8, -3}

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