(x+5)(3x-1)=-21

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Solution for (x+5)(3x-1)=-21 equation: 


Simplifying
(x + 5)(3x + -1) = -21

Reorder the terms:
(5 + x)(3x + -1) = -21

Reorder the terms:
(5 + x)(-1 + 3x) = -21

Multiply (5 + x) * (-1 + 3x)
(5(-1 + 3x) + x(-1 + 3x)) = -21
((-1 * 5 + 3x * 5) + x(-1 + 3x)) = -21
((-5 + 15x) + x(-1 + 3x)) = -21
(-5 + 15x + (-1 * x + 3x * x)) = -21
(-5 + 15x + (-1x + 3x2)) = -21

Combine like terms: 15x + -1x = 14x
(-5 + 14x + 3x2) = -21

Solving
-5 + 14x + 3x2 = -21

Solving for variable 'x'.

Reorder the terms:
-5 + 21 + 14x + 3x2 = -21 + 21

Combine like terms: -5 + 21 = 16
16 + 14x + 3x2 = -21 + 21

Combine like terms: -21 + 21 = 0
16 + 14x + 3x2 = 0

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


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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