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

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

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

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

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

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

Multiply (2 + 3u) * (-1 + u)
-5 + 5u = (2(-1 + u) + 3u * (-1 + u))
-5 + 5u = ((-1 * 2 + u * 2) + 3u * (-1 + u))
-5 + 5u = ((-2 + 2u) + 3u * (-1 + u))
-5 + 5u = (-2 + 2u + (-1 * 3u + u * 3u))
-5 + 5u = (-2 + 2u + (-3u + 3u2))

Combine like terms: 2u + -3u = -1u
-5 + 5u = (-2 + -1u + 3u2)

Solving
-5 + 5u = -2 + -1u + 3u2

Solving for variable 'u'.

Reorder the terms:
-5 + 2 + 5u + u + -3u2 = -2 + -1u + 3u2 + 2 + u + -3u2

Combine like terms: -5 + 2 = -3
-3 + 5u + u + -3u2 = -2 + -1u + 3u2 + 2 + u + -3u2

Combine like terms: 5u + u = 6u
-3 + 6u + -3u2 = -2 + -1u + 3u2 + 2 + u + -3u2

Reorder the terms:
-3 + 6u + -3u2 = -2 + 2 + -1u + u + 3u2 + -3u2

Combine like terms: -2 + 2 = 0
-3 + 6u + -3u2 = 0 + -1u + u + 3u2 + -3u2
-3 + 6u + -3u2 = -1u + u + 3u2 + -3u2

Combine like terms: -1u + u = 0
-3 + 6u + -3u2 = 0 + 3u2 + -3u2
-3 + 6u + -3u2 = 3u2 + -3u2

Combine like terms: 3u2 + -3u2 = 0
-3 + 6u + -3u2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-1 + 2u + -1u2) = 0

Factor a trinomial.
3((-1 + u)(1 + -1u)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-1 + u)' equal to zero and attempt to solve:

Simplifying
-1 + u = 0

Solving
-1 + u = 0

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

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

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

Combine like terms: 0 + 1 = 1
u = 1

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

Simplifying
1 + -1u = 0

Solving
1 + -1u = 0

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

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

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

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

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

Simplifying
u = 1
Solution
u = {1, 1}