(4u+3)2-(6u-3)(u+2)=2u(6+5u)+9

Solution for (4u+3)2-(6u-3)(u+2)=2u(6+5u)+9 equation:

Simplifying
(4u + 3) * 2 + -1(6u + -3)(u + 2) = 2u(6 + 5u) + 9

Reorder the terms:
(3 + 4u) * 2 + -1(6u + -3)(u + 2) = 2u(6 + 5u) + 9

Reorder the terms for easier multiplication:
2(3 + 4u) + -1(6u + -3)(u + 2) = 2u(6 + 5u) + 9
(3 * 2 + 4u * 2) + -1(6u + -3)(u + 2) = 2u(6 + 5u) + 9
(6 + 8u) + -1(6u + -3)(u + 2) = 2u(6 + 5u) + 9

Reorder the terms:
6 + 8u + -1(-3 + 6u)(u + 2) = 2u(6 + 5u) + 9

Reorder the terms:
6 + 8u + -1(-3 + 6u)(2 + u) = 2u(6 + 5u) + 9

Multiply (-3 + 6u) * (2 + u)
6 + 8u + -1(-3(2 + u) + 6u * (2 + u)) = 2u(6 + 5u) + 9
6 + 8u + -1((2 * -3 + u * -3) + 6u * (2 + u)) = 2u(6 + 5u) + 9
6 + 8u + -1((-6 + -3u) + 6u * (2 + u)) = 2u(6 + 5u) + 9
6 + 8u + -1(-6 + -3u + (2 * 6u + u * 6u)) = 2u(6 + 5u) + 9
6 + 8u + -1(-6 + -3u + (12u + 6u2)) = 2u(6 + 5u) + 9

Combine like terms: -3u + 12u = 9u
6 + 8u + -1(-6 + 9u + 6u2) = 2u(6 + 5u) + 9
6 + 8u + (-6 * -1 + 9u * -1 + 6u2 * -1) = 2u(6 + 5u) + 9
6 + 8u + (6 + -9u + -6u2) = 2u(6 + 5u) + 9

Reorder the terms:
6 + 6 + 8u + -9u + -6u2 = 2u(6 + 5u) + 9

Combine like terms: 6 + 6 = 12
12 + 8u + -9u + -6u2 = 2u(6 + 5u) + 9

Combine like terms: 8u + -9u = -1u
12 + -1u + -6u2 = 2u(6 + 5u) + 9
12 + -1u + -6u2 = (6 * 2u + 5u * 2u) + 9
12 + -1u + -6u2 = (12u + 10u2) + 9

Reorder the terms:
12 + -1u + -6u2 = 9 + 12u + 10u2

Solving
12 + -1u + -6u2 = 9 + 12u + 10u2

Solving for variable 'u'.

Reorder the terms:
12 + -9 + -1u + -12u + -6u2 + -10u2 = 9 + 12u + 10u2 + -9 + -12u + -10u2

Combine like terms: 12 + -9 = 3
3 + -1u + -12u + -6u2 + -10u2 = 9 + 12u + 10u2 + -9 + -12u + -10u2

Combine like terms: -1u + -12u = -13u
3 + -13u + -6u2 + -10u2 = 9 + 12u + 10u2 + -9 + -12u + -10u2

Combine like terms: -6u2 + -10u2 = -16u2
3 + -13u + -16u2 = 9 + 12u + 10u2 + -9 + -12u + -10u2

Reorder the terms:
3 + -13u + -16u2 = 9 + -9 + 12u + -12u + 10u2 + -10u2

Combine like terms: 9 + -9 = 0
3 + -13u + -16u2 = 0 + 12u + -12u + 10u2 + -10u2
3 + -13u + -16u2 = 12u + -12u + 10u2 + -10u2

Combine like terms: 12u + -12u = 0
3 + -13u + -16u2 = 0 + 10u2 + -10u2
3 + -13u + -16u2 = 10u2 + -10u2

Combine like terms: 10u2 + -10u2 = 0
3 + -13u + -16u2 = 0

Factor a trinomial.
(3 + -16u)(1 + u) = 0

Subproblem 1
Set the factor '(3 + -16u)' equal to zero and attempt to solve:

Simplifying
3 + -16u = 0

Solving
3 + -16u = 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 + -16u = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -16u = 0 + -3
-16u = 0 + -3

Combine like terms: 0 + -3 = -3
-16u = -3

Divide each side by '-16'.
u = 0.1875

Simplifying
u = 0.1875
Subproblem 2
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
Solution
u = {0.1875, -1}