(-3x-7)(x+8)=0

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Solution for (-3x-7)(x+8)=0 equation: 


Simplifying
(-3x + -7)(x + 8) = 0

Reorder the terms:
(-7 + -3x)(x + 8) = 0

Reorder the terms:
(-7 + -3x)(8 + x) = 0

Multiply (-7 + -3x) * (8 + x)
(-7(8 + x) + -3x * (8 + x)) = 0
((8 * -7 + x * -7) + -3x * (8 + x)) = 0
((-56 + -7x) + -3x * (8 + x)) = 0
(-56 + -7x + (8 * -3x + x * -3x)) = 0
(-56 + -7x + (-24x + -3x2)) = 0

Combine like terms: -7x + -24x = -31x
(-56 + -31x + -3x2) = 0

Solving
-56 + -31x + -3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(56 + 31x + 3x2) = 0

Factor a trinomial.
-1((8 + x)(7 + 3x)) = 0

Ignore the factor -1.

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 '(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 = {-8, -2.333333333}

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