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

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


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

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

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

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

Combine like terms: -3x + -5x = -8x
(-5 + -8x + -3x2) = -1

Solving
-5 + -8x + -3x2 = -1

Solving for variable 'x'.

Reorder the terms:
-5 + 1 + -8x + -3x2 = -1 + 1

Combine like terms: -5 + 1 = -4
-4 + -8x + -3x2 = -1 + 1

Combine like terms: -1 + 1 = 0
-4 + -8x + -3x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(4 + 8x + 3x2) = 0

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

Ignore the factor -1.

Subproblem 1
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

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

Simplifying
2 + 3x = 0

Solving
2 + 3x = 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 + 3x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 3x = 0 + -2
3x = 0 + -2

Combine like terms: 0 + -2 = -2
3x = -2

Divide each side by '3'.
x = -0.6666666667

Simplifying
x = -0.6666666667
Solution
x = {-2, -0.6666666667}

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