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

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


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

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

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

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

Combine like terms: 4x + -3x = 1x
(-12 + 1x + x2) + -14 = (1 + -1x)(x + -2)

Reorder the terms:
-12 + -14 + 1x + x2 = (1 + -1x)(x + -2)

Combine like terms: -12 + -14 = -26
-26 + 1x + x2 = (1 + -1x)(x + -2)

Reorder the terms:
-26 + 1x + x2 = (1 + -1x)(-2 + x)

Multiply (1 + -1x) * (-2 + x)
-26 + 1x + x2 = (1(-2 + x) + -1x * (-2 + x))
-26 + 1x + x2 = ((-2 * 1 + x * 1) + -1x * (-2 + x))
-26 + 1x + x2 = ((-2 + 1x) + -1x * (-2 + x))
-26 + 1x + x2 = (-2 + 1x + (-2 * -1x + x * -1x))
-26 + 1x + x2 = (-2 + 1x + (2x + -1x2))

Combine like terms: 1x + 2x = 3x
-26 + 1x + x2 = (-2 + 3x + -1x2)

Solving
-26 + 1x + x2 = -2 + 3x + -1x2

Solving for variable 'x'.

Reorder the terms:
-26 + 2 + 1x + -3x + x2 + x2 = -2 + 3x + -1x2 + 2 + -3x + x2

Combine like terms: -26 + 2 = -24
-24 + 1x + -3x + x2 + x2 = -2 + 3x + -1x2 + 2 + -3x + x2

Combine like terms: 1x + -3x = -2x
-24 + -2x + x2 + x2 = -2 + 3x + -1x2 + 2 + -3x + x2

Combine like terms: x2 + x2 = 2x2
-24 + -2x + 2x2 = -2 + 3x + -1x2 + 2 + -3x + x2

Reorder the terms:
-24 + -2x + 2x2 = -2 + 2 + 3x + -3x + -1x2 + x2

Combine like terms: -2 + 2 = 0
-24 + -2x + 2x2 = 0 + 3x + -3x + -1x2 + x2
-24 + -2x + 2x2 = 3x + -3x + -1x2 + x2

Combine like terms: 3x + -3x = 0
-24 + -2x + 2x2 = 0 + -1x2 + x2
-24 + -2x + 2x2 = -1x2 + x2

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

Factor out the Greatest Common Factor (GCF), '2'.
2(-12 + -1x + x2) = 0

Factor a trinomial.
2((-3 + -1x)(4 + -1x)) = 0

Ignore the factor 2.

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 '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {-3, 4}

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