10u+7=8u(2u-4)-9

Solution for 10u+7=8u(2u-4)-9 equation:

Simplifying
10u + 7 = 8u(2u + -4) + -9

Reorder the terms:
7 + 10u = 8u(2u + -4) + -9

Reorder the terms:
7 + 10u = 8u(-4 + 2u) + -9
7 + 10u = (-4 * 8u + 2u * 8u) + -9
7 + 10u = (-32u + 16u2) + -9

Reorder the terms:
7 + 10u = -9 + -32u + 16u2

Solving
7 + 10u = -9 + -32u + 16u2

Solving for variable 'u'.

Reorder the terms:
7 + 9 + 10u + 32u + -16u2 = -9 + -32u + 16u2 + 9 + 32u + -16u2

Combine like terms: 7 + 9 = 16
16 + 10u + 32u + -16u2 = -9 + -32u + 16u2 + 9 + 32u + -16u2

Combine like terms: 10u + 32u = 42u
16 + 42u + -16u2 = -9 + -32u + 16u2 + 9 + 32u + -16u2

Reorder the terms:
16 + 42u + -16u2 = -9 + 9 + -32u + 32u + 16u2 + -16u2

Combine like terms: -9 + 9 = 0
16 + 42u + -16u2 = 0 + -32u + 32u + 16u2 + -16u2
16 + 42u + -16u2 = -32u + 32u + 16u2 + -16u2

Combine like terms: -32u + 32u = 0
16 + 42u + -16u2 = 0 + 16u2 + -16u2
16 + 42u + -16u2 = 16u2 + -16u2

Combine like terms: 16u2 + -16u2 = 0
16 + 42u + -16u2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(8 + 21u + -8u2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(8 + 21u + -8u2)' equal to zero and attempt to solve:

Simplifying
8 + 21u + -8u2 = 0

Solving
8 + 21u + -8u2 = 0

Begin completing the square.  Divide all terms by
-8 the coefficient of the squared term: 

Divide each side by '-8'.
-1 + -2.625u + u2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -2.625u + 1 + u2 = 0 + 1

Reorder the terms:
-1 + 1 + -2.625u + u2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -2.625u + u2 = 0 + 1
-2.625u + u2 = 0 + 1

Combine like terms: 0 + 1 = 1
-2.625u + u2 = 1

The u term is -2.625u.  Take half its coefficient (-1.3125).
Square it (1.72265625) and add it to both sides.

Add '1.72265625' to each side of the equation.
-2.625u + 1.72265625 + u2 = 1 + 1.72265625

Reorder the terms:
1.72265625 + -2.625u + u2 = 1 + 1.72265625

Combine like terms: 1 + 1.72265625 = 2.72265625
1.72265625 + -2.625u + u2 = 2.72265625

Factor a perfect square on the left side:
(u + -1.3125)(u + -1.3125) = 2.72265625

Calculate the square root of the right side: 1.650047348

Break this problem into two subproblems by setting 
(u + -1.3125) equal to 1.650047348 and -1.650047348.

Subproblem 1
u + -1.3125 = 1.650047348

Simplifying
u + -1.3125 = 1.650047348

Reorder the terms:
-1.3125 + u = 1.650047348

Solving
-1.3125 + u = 1.650047348

Solving for variable 'u'.

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

Add '1.3125' to each side of the equation.
-1.3125 + 1.3125 + u = 1.650047348 + 1.3125

Combine like terms: -1.3125 + 1.3125 = 0.0000
0.0000 + u = 1.650047348 + 1.3125
u = 1.650047348 + 1.3125

Combine like terms: 1.650047348 + 1.3125 = 2.962547348
u = 2.962547348

Simplifying
u = 2.962547348

Subproblem 2
u + -1.3125 = -1.650047348

Simplifying
u + -1.3125 = -1.650047348

Reorder the terms:
-1.3125 + u = -1.650047348

Solving
-1.3125 + u = -1.650047348

Solving for variable 'u'.

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

Add '1.3125' to each side of the equation.
-1.3125 + 1.3125 + u = -1.650047348 + 1.3125

Combine like terms: -1.3125 + 1.3125 = 0.0000
0.0000 + u = -1.650047348 + 1.3125
u = -1.650047348 + 1.3125

Combine like terms: -1.650047348 + 1.3125 = -0.337547348
u = -0.337547348

Simplifying
u = -0.337547348

Solution
The solution to the problem is based on the solutions
from the subproblems.
u = {2.962547348, -0.337547348}
Solution
u = {2.962547348, -0.337547348}