(x-1)(x+2)-(2x-3)(x+4)-x+14=0

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Solution for (x-1)(x+2)-(2x-3)(x+4)-x+14=0 equation: 


Simplifying
(x + -1)(x + 2) + -1(2x + -3)(x + 4) + -1x + 14 = 0

Reorder the terms:
(-1 + x)(x + 2) + -1(2x + -3)(x + 4) + -1x + 14 = 0

Reorder the terms:
(-1 + x)(2 + x) + -1(2x + -3)(x + 4) + -1x + 14 = 0

Multiply (-1 + x) * (2 + x)
(-1(2 + x) + x(2 + x)) + -1(2x + -3)(x + 4) + -1x + 14 = 0
((2 * -1 + x * -1) + x(2 + x)) + -1(2x + -3)(x + 4) + -1x + 14 = 0
((-2 + -1x) + x(2 + x)) + -1(2x + -3)(x + 4) + -1x + 14 = 0
(-2 + -1x + (2 * x + x * x)) + -1(2x + -3)(x + 4) + -1x + 14 = 0
(-2 + -1x + (2x + x2)) + -1(2x + -3)(x + 4) + -1x + 14 = 0

Combine like terms: -1x + 2x = 1x
(-2 + 1x + x2) + -1(2x + -3)(x + 4) + -1x + 14 = 0

Reorder the terms:
-2 + 1x + x2 + -1(-3 + 2x)(x + 4) + -1x + 14 = 0

Reorder the terms:
-2 + 1x + x2 + -1(-3 + 2x)(4 + x) + -1x + 14 = 0

Multiply (-3 + 2x) * (4 + x)
-2 + 1x + x2 + -1(-3(4 + x) + 2x * (4 + x)) + -1x + 14 = 0
-2 + 1x + x2 + -1((4 * -3 + x * -3) + 2x * (4 + x)) + -1x + 14 = 0
-2 + 1x + x2 + -1((-12 + -3x) + 2x * (4 + x)) + -1x + 14 = 0
-2 + 1x + x2 + -1(-12 + -3x + (4 * 2x + x * 2x)) + -1x + 14 = 0
-2 + 1x + x2 + -1(-12 + -3x + (8x + 2x2)) + -1x + 14 = 0

Combine like terms: -3x + 8x = 5x
-2 + 1x + x2 + -1(-12 + 5x + 2x2) + -1x + 14 = 0
-2 + 1x + x2 + (-12 * -1 + 5x * -1 + 2x2 * -1) + -1x + 14 = 0
-2 + 1x + x2 + (12 + -5x + -2x2) + -1x + 14 = 0

Reorder the terms:
-2 + 12 + 14 + 1x + -5x + -1x + x2 + -2x2 = 0

Combine like terms: -2 + 12 = 10
10 + 14 + 1x + -5x + -1x + x2 + -2x2 = 0

Combine like terms: 10 + 14 = 24
24 + 1x + -5x + -1x + x2 + -2x2 = 0

Combine like terms: 1x + -5x = -4x
24 + -4x + -1x + x2 + -2x2 = 0

Combine like terms: -4x + -1x = -5x
24 + -5x + x2 + -2x2 = 0

Combine like terms: x2 + -2x2 = -1x2
24 + -5x + -1x2 = 0

Solving
24 + -5x + -1x2 = 0

Solving for variable 'x'.

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


Subproblem 1
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 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 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3

Subproblem 2
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
Solution
x = {3, -8}

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