(x+5)(x-1)=(2x+3)(x-1)

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Solution for (x+5)(x-1)=(2x+3)(x-1) equation:


Simplifying
(x + 5)(x + -1) = (2x + 3)(x + -1)

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

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

Multiply (5 + x) * (-1 + x)
(5(-1 + x) + x(-1 + x)) = (2x + 3)(x + -1)
((-1 * 5 + x * 5) + x(-1 + x)) = (2x + 3)(x + -1)
((-5 + 5x) + x(-1 + x)) = (2x + 3)(x + -1)
(-5 + 5x + (-1 * x + x * x)) = (2x + 3)(x + -1)
(-5 + 5x + (-1x + x2)) = (2x + 3)(x + -1)

Combine like terms: 5x + -1x = 4x
(-5 + 4x + x2) = (2x + 3)(x + -1)

Reorder the terms:
-5 + 4x + x2 = (3 + 2x)(x + -1)

Reorder the terms:
-5 + 4x + x2 = (3 + 2x)(-1 + x)

Multiply (3 + 2x) * (-1 + x)
-5 + 4x + x2 = (3(-1 + x) + 2x * (-1 + x))
-5 + 4x + x2 = ((-1 * 3 + x * 3) + 2x * (-1 + x))
-5 + 4x + x2 = ((-3 + 3x) + 2x * (-1 + x))
-5 + 4x + x2 = (-3 + 3x + (-1 * 2x + x * 2x))
-5 + 4x + x2 = (-3 + 3x + (-2x + 2x2))

Combine like terms: 3x + -2x = 1x
-5 + 4x + x2 = (-3 + 1x + 2x2)

Solving
-5 + 4x + x2 = -3 + 1x + 2x2

Solving for variable 'x'.

Reorder the terms:
-5 + 3 + 4x + -1x + x2 + -2x2 = -3 + 1x + 2x2 + 3 + -1x + -2x2

Combine like terms: -5 + 3 = -2
-2 + 4x + -1x + x2 + -2x2 = -3 + 1x + 2x2 + 3 + -1x + -2x2

Combine like terms: 4x + -1x = 3x
-2 + 3x + x2 + -2x2 = -3 + 1x + 2x2 + 3 + -1x + -2x2

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

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

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

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

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

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

Subproblem 1

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

Subproblem 2

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

Solution

x = {2, 1}

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