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

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


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

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

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

Multiply (1 + 2x) * (-5 + x)
(1(-5 + x) + 2x * (-5 + x)) = (x + -1)(x + -2)
((-5 * 1 + x * 1) + 2x * (-5 + x)) = (x + -1)(x + -2)
((-5 + 1x) + 2x * (-5 + x)) = (x + -1)(x + -2)
(-5 + 1x + (-5 * 2x + x * 2x)) = (x + -1)(x + -2)
(-5 + 1x + (-10x + 2x2)) = (x + -1)(x + -2)

Combine like terms: 1x + -10x = -9x
(-5 + -9x + 2x2) = (x + -1)(x + -2)

Reorder the terms:
-5 + -9x + 2x2 = (-1 + x)(x + -2)

Reorder the terms:
-5 + -9x + 2x2 = (-1 + x)(-2 + x)

Multiply (-1 + x) * (-2 + x)
-5 + -9x + 2x2 = (-1(-2 + x) + x(-2 + x))
-5 + -9x + 2x2 = ((-2 * -1 + x * -1) + x(-2 + x))
-5 + -9x + 2x2 = ((2 + -1x) + x(-2 + x))
-5 + -9x + 2x2 = (2 + -1x + (-2 * x + x * x))
-5 + -9x + 2x2 = (2 + -1x + (-2x + x2))

Combine like terms: -1x + -2x = -3x
-5 + -9x + 2x2 = (2 + -3x + x2)

Solving
-5 + -9x + 2x2 = 2 + -3x + x2

Solving for variable 'x'.

Reorder the terms:
-5 + -2 + -9x + 3x + 2x2 + -1x2 = 2 + -3x + x2 + -2 + 3x + -1x2

Combine like terms: -5 + -2 = -7
-7 + -9x + 3x + 2x2 + -1x2 = 2 + -3x + x2 + -2 + 3x + -1x2

Combine like terms: -9x + 3x = -6x
-7 + -6x + 2x2 + -1x2 = 2 + -3x + x2 + -2 + 3x + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
-7 + -6x + 1x2 = 2 + -3x + x2 + -2 + 3x + -1x2

Reorder the terms:
-7 + -6x + 1x2 = 2 + -2 + -3x + 3x + x2 + -1x2

Combine like terms: 2 + -2 = 0
-7 + -6x + 1x2 = 0 + -3x + 3x + x2 + -1x2
-7 + -6x + 1x2 = -3x + 3x + x2 + -1x2

Combine like terms: -3x + 3x = 0
-7 + -6x + 1x2 = 0 + x2 + -1x2
-7 + -6x + 1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-7 + -6x + 1x2 = 0

Factor a trinomial.
(-1 + -1x)(7 + -1x) = 0


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 '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {-1, 7}

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