(h+1)(h-1)=(h-1)(2h-1)

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Solution for (h+1)(h-1)=(h-1)(2h-1) equation:


Simplifying
(h + 1)(h + -1) = (h + -1)(2h + -1)

Reorder the terms:
(1 + h)(h + -1) = (h + -1)(2h + -1)

Reorder the terms:
(1 + h)(-1 + h) = (h + -1)(2h + -1)

Multiply (1 + h) * (-1 + h)
(1(-1 + h) + h(-1 + h)) = (h + -1)(2h + -1)
((-1 * 1 + h * 1) + h(-1 + h)) = (h + -1)(2h + -1)
((-1 + 1h) + h(-1 + h)) = (h + -1)(2h + -1)
(-1 + 1h + (-1 * h + h * h)) = (h + -1)(2h + -1)
(-1 + 1h + (-1h + h2)) = (h + -1)(2h + -1)

Combine like terms: 1h + -1h = 0
(-1 + 0 + h2) = (h + -1)(2h + -1)
(-1 + h2) = (h + -1)(2h + -1)

Reorder the terms:
-1 + h2 = (-1 + h)(2h + -1)

Reorder the terms:
-1 + h2 = (-1 + h)(-1 + 2h)

Multiply (-1 + h) * (-1 + 2h)
-1 + h2 = (-1(-1 + 2h) + h(-1 + 2h))
-1 + h2 = ((-1 * -1 + 2h * -1) + h(-1 + 2h))
-1 + h2 = ((1 + -2h) + h(-1 + 2h))
-1 + h2 = (1 + -2h + (-1 * h + 2h * h))
-1 + h2 = (1 + -2h + (-1h + 2h2))

Combine like terms: -2h + -1h = -3h
-1 + h2 = (1 + -3h + 2h2)

Solving
-1 + h2 = 1 + -3h + 2h2

Solving for variable 'h'.

Reorder the terms:
-1 + -1 + 3h + h2 + -2h2 = 1 + -3h + 2h2 + -1 + 3h + -2h2

Combine like terms: -1 + -1 = -2
-2 + 3h + h2 + -2h2 = 1 + -3h + 2h2 + -1 + 3h + -2h2

Combine like terms: h2 + -2h2 = -1h2
-2 + 3h + -1h2 = 1 + -3h + 2h2 + -1 + 3h + -2h2

Reorder the terms:
-2 + 3h + -1h2 = 1 + -1 + -3h + 3h + 2h2 + -2h2

Combine like terms: 1 + -1 = 0
-2 + 3h + -1h2 = 0 + -3h + 3h + 2h2 + -2h2
-2 + 3h + -1h2 = -3h + 3h + 2h2 + -2h2

Combine like terms: -3h + 3h = 0
-2 + 3h + -1h2 = 0 + 2h2 + -2h2
-2 + 3h + -1h2 = 2h2 + -2h2

Combine like terms: 2h2 + -2h2 = 0
-2 + 3h + -1h2 = 0

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

Subproblem 1

Set the factor '(-2 + h)' equal to zero and attempt to solve: Simplifying -2 + h = 0 Solving -2 + h = 0 Move all terms containing h to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + h = 0 + 2 Combine like terms: -2 + 2 = 0 0 + h = 0 + 2 h = 0 + 2 Combine like terms: 0 + 2 = 2 h = 2 Simplifying h = 2

Subproblem 2

Set the factor '(1 + -1h)' equal to zero and attempt to solve: Simplifying 1 + -1h = 0 Solving 1 + -1h = 0 Move all terms containing h to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1h = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1h = 0 + -1 -1h = 0 + -1 Combine like terms: 0 + -1 = -1 -1h = -1 Divide each side by '-1'. h = 1 Simplifying h = 1

Solution

h = {2, 1}

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