23-23x=(5x+2)(x-1)

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Solution for 23-23x=(5x+2)(x-1) equation: 


Simplifying
23 + -23x = (5x + 2)(x + -1)

Reorder the terms:
23 + -23x = (2 + 5x)(x + -1)

Reorder the terms:
23 + -23x = (2 + 5x)(-1 + x)

Multiply (2 + 5x) * (-1 + x)
23 + -23x = (2(-1 + x) + 5x * (-1 + x))
23 + -23x = ((-1 * 2 + x * 2) + 5x * (-1 + x))
23 + -23x = ((-2 + 2x) + 5x * (-1 + x))
23 + -23x = (-2 + 2x + (-1 * 5x + x * 5x))
23 + -23x = (-2 + 2x + (-5x + 5x2))

Combine like terms: 2x + -5x = -3x
23 + -23x = (-2 + -3x + 5x2)

Solving
23 + -23x = -2 + -3x + 5x2

Solving for variable 'x'.

Reorder the terms:
23 + 2 + -23x + 3x + -5x2 = -2 + -3x + 5x2 + 2 + 3x + -5x2

Combine like terms: 23 + 2 = 25
25 + -23x + 3x + -5x2 = -2 + -3x + 5x2 + 2 + 3x + -5x2

Combine like terms: -23x + 3x = -20x
25 + -20x + -5x2 = -2 + -3x + 5x2 + 2 + 3x + -5x2

Reorder the terms:
25 + -20x + -5x2 = -2 + 2 + -3x + 3x + 5x2 + -5x2

Combine like terms: -2 + 2 = 0
25 + -20x + -5x2 = 0 + -3x + 3x + 5x2 + -5x2
25 + -20x + -5x2 = -3x + 3x + 5x2 + -5x2

Combine like terms: -3x + 3x = 0
25 + -20x + -5x2 = 0 + 5x2 + -5x2
25 + -20x + -5x2 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
25 + -20x + -5x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(5 + -4x + -1x2) = 0

Factor a trinomial.
5((1 + -1x)(5 + x)) = 0

Ignore the factor 5.

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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

Simplifying
x = 1

Subproblem 2
Set the factor '(5 + x)' equal to zero and attempt to solve:

Simplifying
5 + x = 0

Solving
5 + x = 0

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

Add '-5' to each side of the equation.
5 + -5 + x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + x = 0 + -5
x = 0 + -5

Combine like terms: 0 + -5 = -5
x = -5

Simplifying
x = -5
Solution
x = {1, -5}

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