8(u+2)(u+1)-7(u+1)=3(u+2)

Solution for 8(u+2)(u+1)-7(u+1)=3(u+2) equation:

Simplifying
8(u + 2)(u + 1) + -7(u + 1) = 3(u + 2)

Reorder the terms:
8(2 + u)(u + 1) + -7(u + 1) = 3(u + 2)

Reorder the terms:
8(2 + u)(1 + u) + -7(u + 1) = 3(u + 2)

Multiply (2 + u) * (1 + u)
8(2(1 + u) + u(1 + u)) + -7(u + 1) = 3(u + 2)
8((1 * 2 + u * 2) + u(1 + u)) + -7(u + 1) = 3(u + 2)
8((2 + 2u) + u(1 + u)) + -7(u + 1) = 3(u + 2)
8(2 + 2u + (1 * u + u * u)) + -7(u + 1) = 3(u + 2)
8(2 + 2u + (1u + u2)) + -7(u + 1) = 3(u + 2)

Combine like terms: 2u + 1u = 3u
8(2 + 3u + u2) + -7(u + 1) = 3(u + 2)
(2 * 8 + 3u * 8 + u2 * 8) + -7(u + 1) = 3(u + 2)
(16 + 24u + 8u2) + -7(u + 1) = 3(u + 2)

Reorder the terms:
16 + 24u + 8u2 + -7(1 + u) = 3(u + 2)
16 + 24u + 8u2 + (1 * -7 + u * -7) = 3(u + 2)
16 + 24u + 8u2 + (-7 + -7u) = 3(u + 2)

Reorder the terms:
16 + -7 + 24u + -7u + 8u2 = 3(u + 2)

Combine like terms: 16 + -7 = 9
9 + 24u + -7u + 8u2 = 3(u + 2)

Combine like terms: 24u + -7u = 17u
9 + 17u + 8u2 = 3(u + 2)

Reorder the terms:
9 + 17u + 8u2 = 3(2 + u)
9 + 17u + 8u2 = (2 * 3 + u * 3)
9 + 17u + 8u2 = (6 + 3u)

Solving
9 + 17u + 8u2 = 6 + 3u

Solving for variable 'u'.

Reorder the terms:
9 + -6 + 17u + -3u + 8u2 = 6 + 3u + -6 + -3u

Combine like terms: 9 + -6 = 3
3 + 17u + -3u + 8u2 = 6 + 3u + -6 + -3u

Combine like terms: 17u + -3u = 14u
3 + 14u + 8u2 = 6 + 3u + -6 + -3u

Reorder the terms:
3 + 14u + 8u2 = 6 + -6 + 3u + -3u

Combine like terms: 6 + -6 = 0
3 + 14u + 8u2 = 0 + 3u + -3u
3 + 14u + 8u2 = 3u + -3u

Combine like terms: 3u + -3u = 0
3 + 14u + 8u2 = 0

Factor a trinomial.
(3 + 2u)(1 + 4u) = 0

Subproblem 1
Set the factor '(3 + 2u)' equal to zero and attempt to solve:

Simplifying
3 + 2u = 0

Solving
3 + 2u = 0

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

Add '-3' to each side of the equation.
3 + -3 + 2u = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2u = 0 + -3
2u = 0 + -3

Combine like terms: 0 + -3 = -3
2u = -3

Divide each side by '2'.
u = -1.5

Simplifying
u = -1.5
Subproblem 2
Set the factor '(1 + 4u)' equal to zero and attempt to solve:

Simplifying
1 + 4u = 0

Solving
1 + 4u = 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 + 4u = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 4u = 0 + -1
4u = 0 + -1

Combine like terms: 0 + -1 = -1
4u = -1

Divide each side by '4'.
u = -0.25

Simplifying
u = -0.25
Solution
u = {-1.5, -0.25}