4(6x+5)(7x-8)+8(x+9)=

Solution for 4(6x+5)(7x-8)+8(x+9)= equation:

Simplifying
4(6x + 5)(7x + -8) + 8(x + 9) = 0

Reorder the terms:
4(5 + 6x)(7x + -8) + 8(x + 9) = 0

Reorder the terms:
4(5 + 6x)(-8 + 7x) + 8(x + 9) = 0

Multiply (5 + 6x) * (-8 + 7x)
4(5(-8 + 7x) + 6x * (-8 + 7x)) + 8(x + 9) = 0
4((-8 * 5 + 7x * 5) + 6x * (-8 + 7x)) + 8(x + 9) = 0
4((-40 + 35x) + 6x * (-8 + 7x)) + 8(x + 9) = 0
4(-40 + 35x + (-8 * 6x + 7x * 6x)) + 8(x + 9) = 0
4(-40 + 35x + (-48x + 42x2)) + 8(x + 9) = 0

Combine like terms: 35x + -48x = -13x
4(-40 + -13x + 42x2) + 8(x + 9) = 0
(-40 * 4 + -13x * 4 + 42x2 * 4) + 8(x + 9) = 0
(-160 + -52x + 168x2) + 8(x + 9) = 0

Reorder the terms:
-160 + -52x + 168x2 + 8(9 + x) = 0
-160 + -52x + 168x2 + (9 * 8 + x * 8) = 0
-160 + -52x + 168x2 + (72 + 8x) = 0

Reorder the terms:
-160 + 72 + -52x + 8x + 168x2 = 0

Combine like terms: -160 + 72 = -88
-88 + -52x + 8x + 168x2 = 0

Combine like terms: -52x + 8x = -44x
-88 + -44x + 168x2 = 0

Solving
-88 + -44x + 168x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-22 + -11x + 42x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-22 + -11x + 42x2)' equal to zero and attempt to solve:

Simplifying
-22 + -11x + 42x2 = 0

Solving
-22 + -11x + 42x2 = 0

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

Divide each side by '42'.
-0.5238095238 + -0.2619047619x + x2 = 0

Move the constant term to the right:

Add '0.5238095238' to each side of the equation.
-0.5238095238 + -0.2619047619x + 0.5238095238 + x2 = 0 + 0.5238095238

Reorder the terms:
-0.5238095238 + 0.5238095238 + -0.2619047619x + x2 = 0 + 0.5238095238

Combine like terms: -0.5238095238 + 0.5238095238 = 0.0000000000
0.0000000000 + -0.2619047619x + x2 = 0 + 0.5238095238
-0.2619047619x + x2 = 0 + 0.5238095238

Combine like terms: 0 + 0.5238095238 = 0.5238095238
-0.2619047619x + x2 = 0.5238095238

The x term is -0.2619047619x.  Take half its coefficient (-0.130952381).
Square it (0.01714852609) and add it to both sides.

Add '0.01714852609' to each side of the equation.
-0.2619047619x + 0.01714852609 + x2 = 0.5238095238 + 0.01714852609

Reorder the terms:
0.01714852609 + -0.2619047619x + x2 = 0.5238095238 + 0.01714852609

Combine like terms: 0.5238095238 + 0.01714852609 = 0.54095804989
0.01714852609 + -0.2619047619x + x2 = 0.54095804989

Factor a perfect square on the left side:
(x + -0.130952381)(x + -0.130952381) = 0.54095804989

Calculate the square root of the right side: 0.735498504

Break this problem into two subproblems by setting 
(x + -0.130952381) equal to 0.735498504 and -0.735498504.

Subproblem 1
x + -0.130952381 = 0.735498504

Simplifying
x + -0.130952381 = 0.735498504

Reorder the terms:
-0.130952381 + x = 0.735498504

Solving
-0.130952381 + x = 0.735498504

Solving for variable 'x'.

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

Add '0.130952381' to each side of the equation.
-0.130952381 + 0.130952381 + x = 0.735498504 + 0.130952381

Combine like terms: -0.130952381 + 0.130952381 = 0.000000000
0.000000000 + x = 0.735498504 + 0.130952381
x = 0.735498504 + 0.130952381

Combine like terms: 0.735498504 + 0.130952381 = 0.866450885
x = 0.866450885

Simplifying
x = 0.866450885

Subproblem 2
x + -0.130952381 = -0.735498504

Simplifying
x + -0.130952381 = -0.735498504

Reorder the terms:
-0.130952381 + x = -0.735498504

Solving
-0.130952381 + x = -0.735498504

Solving for variable 'x'.

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

Add '0.130952381' to each side of the equation.
-0.130952381 + 0.130952381 + x = -0.735498504 + 0.130952381

Combine like terms: -0.130952381 + 0.130952381 = 0.000000000
0.000000000 + x = -0.735498504 + 0.130952381
x = -0.735498504 + 0.130952381

Combine like terms: -0.735498504 + 0.130952381 = -0.604546123
x = -0.604546123

Simplifying
x = -0.604546123

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.866450885, -0.604546123}
Solution
x = {0.866450885, -0.604546123}