(2u+3)(4u-18)=114

Solution for (2u+3)(4u-18)=114 equation:

Simplifying
(2u + 3)(4u + -18) = 114

Reorder the terms:
(3 + 2u)(4u + -18) = 114

Reorder the terms:
(3 + 2u)(-18 + 4u) = 114

Multiply (3 + 2u) * (-18 + 4u)
(3(-18 + 4u) + 2u * (-18 + 4u)) = 114
((-18 * 3 + 4u * 3) + 2u * (-18 + 4u)) = 114
((-54 + 12u) + 2u * (-18 + 4u)) = 114
(-54 + 12u + (-18 * 2u + 4u * 2u)) = 114
(-54 + 12u + (-36u + 8u2)) = 114

Combine like terms: 12u + -36u = -24u
(-54 + -24u + 8u2) = 114

Solving
-54 + -24u + 8u2 = 114

Solving for variable 'u'.

Reorder the terms:
-54 + -114 + -24u + 8u2 = 114 + -114

Combine like terms: -54 + -114 = -168
-168 + -24u + 8u2 = 114 + -114

Combine like terms: 114 + -114 = 0
-168 + -24u + 8u2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(-21 + -3u + u2) = 0

Ignore the factor 8.
Subproblem 1
Set the factor '(-21 + -3u + u2)' equal to zero and attempt to solve:

Simplifying
-21 + -3u + u2 = 0

Solving
-21 + -3u + u2 = 0

Begin completing the square.

Move the constant term to the right:

Add '21' to each side of the equation.
-21 + -3u + 21 + u2 = 0 + 21

Reorder the terms:
-21 + 21 + -3u + u2 = 0 + 21

Combine like terms: -21 + 21 = 0
0 + -3u + u2 = 0 + 21
-3u + u2 = 0 + 21

Combine like terms: 0 + 21 = 21
-3u + u2 = 21

The u term is -3u.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3u + 2.25 + u2 = 21 + 2.25

Reorder the terms:
2.25 + -3u + u2 = 21 + 2.25

Combine like terms: 21 + 2.25 = 23.25
2.25 + -3u + u2 = 23.25

Factor a perfect square on the left side:
(u + -1.5)(u + -1.5) = 23.25

Calculate the square root of the right side: 4.82182538

Break this problem into two subproblems by setting 
(u + -1.5) equal to 4.82182538 and -4.82182538.

Subproblem 1
u + -1.5 = 4.82182538

Simplifying
u + -1.5 = 4.82182538

Reorder the terms:
-1.5 + u = 4.82182538

Solving
-1.5 + u = 4.82182538

Solving for variable 'u'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + u = 4.82182538 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + u = 4.82182538 + 1.5
u = 4.82182538 + 1.5

Combine like terms: 4.82182538 + 1.5 = 6.32182538
u = 6.32182538

Simplifying
u = 6.32182538

Subproblem 2
u + -1.5 = -4.82182538

Simplifying
u + -1.5 = -4.82182538

Reorder the terms:
-1.5 + u = -4.82182538

Solving
-1.5 + u = -4.82182538

Solving for variable 'u'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + u = -4.82182538 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + u = -4.82182538 + 1.5
u = -4.82182538 + 1.5

Combine like terms: -4.82182538 + 1.5 = -3.32182538
u = -3.32182538

Simplifying
u = -3.32182538

Solution
The solution to the problem is based on the solutions
from the subproblems.
u = {6.32182538, -3.32182538}
Solution
u = {6.32182538, -3.32182538}