(2u-1)(5u+6)=(u-2)(u+3)

Solution for (2u-1)(5u+6)=(u-2)(u+3) equation:

Simplifying
(2u + -1)(5u + 6) = (u + -2)(u + 3)

Reorder the terms:
(-1 + 2u)(5u + 6) = (u + -2)(u + 3)

Reorder the terms:
(-1 + 2u)(6 + 5u) = (u + -2)(u + 3)

Multiply (-1 + 2u) * (6 + 5u)
(-1(6 + 5u) + 2u * (6 + 5u)) = (u + -2)(u + 3)
((6 * -1 + 5u * -1) + 2u * (6 + 5u)) = (u + -2)(u + 3)
((-6 + -5u) + 2u * (6 + 5u)) = (u + -2)(u + 3)
(-6 + -5u + (6 * 2u + 5u * 2u)) = (u + -2)(u + 3)
(-6 + -5u + (12u + 10u2)) = (u + -2)(u + 3)

Combine like terms: -5u + 12u = 7u
(-6 + 7u + 10u2) = (u + -2)(u + 3)

Reorder the terms:
-6 + 7u + 10u2 = (-2 + u)(u + 3)

Reorder the terms:
-6 + 7u + 10u2 = (-2 + u)(3 + u)

Multiply (-2 + u) * (3 + u)
-6 + 7u + 10u2 = (-2(3 + u) + u(3 + u))
-6 + 7u + 10u2 = ((3 * -2 + u * -2) + u(3 + u))
-6 + 7u + 10u2 = ((-6 + -2u) + u(3 + u))
-6 + 7u + 10u2 = (-6 + -2u + (3 * u + u * u))
-6 + 7u + 10u2 = (-6 + -2u + (3u + u2))

Combine like terms: -2u + 3u = 1u
-6 + 7u + 10u2 = (-6 + 1u + u2)

Add '6' to each side of the equation.
-6 + 7u + 6 + 10u2 = -6 + 1u + 6 + u2

Reorder the terms:
-6 + 6 + 7u + 10u2 = -6 + 1u + 6 + u2

Combine like terms: -6 + 6 = 0
0 + 7u + 10u2 = -6 + 1u + 6 + u2
7u + 10u2 = -6 + 1u + 6 + u2

Reorder the terms:
7u + 10u2 = -6 + 6 + 1u + u2

Combine like terms: -6 + 6 = 0
7u + 10u2 = 0 + 1u + u2
7u + 10u2 = 1u + u2

Solving
7u + 10u2 = 1u + u2

Solving for variable 'u'.

Reorder the terms:
7u + -1u + 10u2 + -1u2 = 1u + u2 + -1u + -1u2

Combine like terms: 7u + -1u = 6u
6u + 10u2 + -1u2 = 1u + u2 + -1u + -1u2

Combine like terms: 10u2 + -1u2 = 9u2
6u + 9u2 = 1u + u2 + -1u + -1u2

Reorder the terms:
6u + 9u2 = 1u + -1u + u2 + -1u2

Combine like terms: 1u + -1u = 0
6u + 9u2 = 0 + u2 + -1u2
6u + 9u2 = u2 + -1u2

Combine like terms: u2 + -1u2 = 0
6u + 9u2 = 0

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

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

Simplifying
u = 0

Solving
u = 0

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

Simplifying
u = 0
Subproblem 2
Set the factor '(2 + 3u)' equal to zero and attempt to solve:

Simplifying
2 + 3u = 0

Solving
2 + 3u = 0

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

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

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

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

Divide each side by '3'.
u = -0.6666666667

Simplifying
u = -0.6666666667
Solution
u = {0, -0.6666666667}