-19-17x=(3x+1)(x-1)

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Solution for -19-17x=(3x+1)(x-1) equation: 


Simplifying
-19 + -17x = (3x + 1)(x + -1)

Reorder the terms:
-19 + -17x = (1 + 3x)(x + -1)

Reorder the terms:
-19 + -17x = (1 + 3x)(-1 + x)

Multiply (1 + 3x) * (-1 + x)
-19 + -17x = (1(-1 + x) + 3x * (-1 + x))
-19 + -17x = ((-1 * 1 + x * 1) + 3x * (-1 + x))
-19 + -17x = ((-1 + 1x) + 3x * (-1 + x))
-19 + -17x = (-1 + 1x + (-1 * 3x + x * 3x))
-19 + -17x = (-1 + 1x + (-3x + 3x2))

Combine like terms: 1x + -3x = -2x
-19 + -17x = (-1 + -2x + 3x2)

Solving
-19 + -17x = -1 + -2x + 3x2

Solving for variable 'x'.

Reorder the terms:
-19 + 1 + -17x + 2x + -3x2 = -1 + -2x + 3x2 + 1 + 2x + -3x2

Combine like terms: -19 + 1 = -18
-18 + -17x + 2x + -3x2 = -1 + -2x + 3x2 + 1 + 2x + -3x2

Combine like terms: -17x + 2x = -15x
-18 + -15x + -3x2 = -1 + -2x + 3x2 + 1 + 2x + -3x2

Reorder the terms:
-18 + -15x + -3x2 = -1 + 1 + -2x + 2x + 3x2 + -3x2

Combine like terms: -1 + 1 = 0
-18 + -15x + -3x2 = 0 + -2x + 2x + 3x2 + -3x2
-18 + -15x + -3x2 = -2x + 2x + 3x2 + -3x2

Combine like terms: -2x + 2x = 0
-18 + -15x + -3x2 = 0 + 3x2 + -3x2
-18 + -15x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
-18 + -15x + -3x2 = 0

Factor out the Greatest Common Factor (GCF), '-3'.
-3(6 + 5x + x2) = 0

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

Ignore the factor -3.

Subproblem 1
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

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 = {-3, -2}

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