-8n(7n-3)=-88

Solution for -8n(7n-3)=-88 equation:

Simplifying
-8n(7n + -3) = -88

Reorder the terms:
-8n(-3 + 7n) = -88
(-3 * -8n + 7n * -8n) = -88
(24n + -56n2) = -88

Solving
24n + -56n2 = -88

Solving for variable 'n'.

Reorder the terms:
88 + 24n + -56n2 = -88 + 88

Combine like terms: -88 + 88 = 0
88 + 24n + -56n2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(11 + 3n + -7n2) = 0

Ignore the factor 8.
Subproblem 1
Set the factor '(11 + 3n + -7n2)' equal to zero and attempt to solve:

Simplifying
11 + 3n + -7n2 = 0

Solving
11 + 3n + -7n2 = 0

Begin completing the square.  Divide all terms by
-7 the coefficient of the squared term: 

Divide each side by '-7'.
-1.571428571 + -0.4285714286n + n2 = 0

Move the constant term to the right:

Add '1.571428571' to each side of the equation.
-1.571428571 + -0.4285714286n + 1.571428571 + n2 = 0 + 1.571428571

Reorder the terms:
-1.571428571 + 1.571428571 + -0.4285714286n + n2 = 0 + 1.571428571

Combine like terms: -1.571428571 + 1.571428571 = 0.000000000
0.000000000 + -0.4285714286n + n2 = 0 + 1.571428571
-0.4285714286n + n2 = 0 + 1.571428571

Combine like terms: 0 + 1.571428571 = 1.571428571
-0.4285714286n + n2 = 1.571428571

The n term is -0.4285714286n.  Take half its coefficient (-0.2142857143).
Square it (0.04591836735) and add it to both sides.

Add '0.04591836735' to each side of the equation.
-0.4285714286n + 0.04591836735 + n2 = 1.571428571 + 0.04591836735

Reorder the terms:
0.04591836735 + -0.4285714286n + n2 = 1.571428571 + 0.04591836735

Combine like terms: 1.571428571 + 0.04591836735 = 1.61734693835
0.04591836735 + -0.4285714286n + n2 = 1.61734693835

Factor a perfect square on the left side:
(n + -0.2142857143)(n + -0.2142857143) = 1.61734693835

Calculate the square root of the right side: 1.271749558

Break this problem into two subproblems by setting 
(n + -0.2142857143) equal to 1.271749558 and -1.271749558.

Subproblem 1
n + -0.2142857143 = 1.271749558

Simplifying
n + -0.2142857143 = 1.271749558

Reorder the terms:
-0.2142857143 + n = 1.271749558

Solving
-0.2142857143 + n = 1.271749558

Solving for variable 'n'.

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

Add '0.2142857143' to each side of the equation.
-0.2142857143 + 0.2142857143 + n = 1.271749558 + 0.2142857143

Combine like terms: -0.2142857143 + 0.2142857143 = 0.0000000000
0.0000000000 + n = 1.271749558 + 0.2142857143
n = 1.271749558 + 0.2142857143

Combine like terms: 1.271749558 + 0.2142857143 = 1.4860352723
n = 1.4860352723

Simplifying
n = 1.4860352723

Subproblem 2
n + -0.2142857143 = -1.271749558

Simplifying
n + -0.2142857143 = -1.271749558

Reorder the terms:
-0.2142857143 + n = -1.271749558

Solving
-0.2142857143 + n = -1.271749558

Solving for variable 'n'.

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

Add '0.2142857143' to each side of the equation.
-0.2142857143 + 0.2142857143 + n = -1.271749558 + 0.2142857143

Combine like terms: -0.2142857143 + 0.2142857143 = 0.0000000000
0.0000000000 + n = -1.271749558 + 0.2142857143
n = -1.271749558 + 0.2142857143

Combine like terms: -1.271749558 + 0.2142857143 = -1.0574638437
n = -1.0574638437

Simplifying
n = -1.0574638437

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {1.4860352723, -1.0574638437}
Solution
n = {1.4860352723, -1.0574638437}