2(k-1)(k+1)=3(k-1)

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

Simplifying
2(k + -1)(k + 1) = 3(k + -1)

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

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

Multiply (-1 + k) * (1 + k)
2(-1(1 + k) + k(1 + k)) = 3(k + -1)
2((1 * -1 + k * -1) + k(1 + k)) = 3(k + -1)
2((-1 + -1k) + k(1 + k)) = 3(k + -1)
2(-1 + -1k + (1 * k + k * k)) = 3(k + -1)
2(-1 + -1k + (1k + k2)) = 3(k + -1)

Combine like terms: -1k + 1k = 0
2(-1 + 0 + k2) = 3(k + -1)
2(-1 + k2) = 3(k + -1)
(-1 * 2 + k2 * 2) = 3(k + -1)
(-2 + 2k2) = 3(k + -1)

Reorder the terms:
-2 + 2k2 = 3(-1 + k)
-2 + 2k2 = (-1 * 3 + k * 3)
-2 + 2k2 = (-3 + 3k)

Solving
-2 + 2k2 = -3 + 3k

Solving for variable 'k'.

Reorder the terms:
-2 + 3 + -3k + 2k2 = -3 + 3k + 3 + -3k

Combine like terms: -2 + 3 = 1
1 + -3k + 2k2 = -3 + 3k + 3 + -3k

Reorder the terms:
1 + -3k + 2k2 = -3 + 3 + 3k + -3k

Combine like terms: -3 + 3 = 0
1 + -3k + 2k2 = 0 + 3k + -3k
1 + -3k + 2k2 = 3k + -3k

Combine like terms: 3k + -3k = 0
1 + -3k + 2k2 = 0

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

Subproblem 1
Set the factor '(1 + -2k)' equal to zero and attempt to solve:

Simplifying
1 + -2k = 0

Solving
1 + -2k = 0

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

Add '-1' to each side of the equation.
1 + -1 + -2k = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2k = 0 + -1
-2k = 0 + -1

Combine like terms: 0 + -1 = -1
-2k = -1

Divide each side by '-2'.
k = 0.5

Simplifying
k = 0.5
Subproblem 2
Set the factor '(1 + -1k)' equal to zero and attempt to solve:

Simplifying
1 + -1k = 0

Solving
1 + -1k = 0

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

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

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

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

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

Simplifying
k = 1
Solution
k = {0.5, 1}