154=-4(8+6r)24r

Solution for 154=-4(8+6r)24r equation:

Simplifying
154 = -4(8 + 6r) * 24r

Reorder the terms for easier multiplication:
154 = -4 * 24r(8 + 6r)

Multiply -4 * 24
154 = -96r(8 + 6r)
154 = (8 * -96r + 6r * -96r)
154 = (-768r + -576r2)

Solving
154 = -768r + -576r2

Solving for variable 'r'.

Reorder the terms:
154 + 768r + 576r2 = -768r + 768r + -576r2 + 576r2

Combine like terms: -768r + 768r = 0
154 + 768r + 576r2 = 0 + -576r2 + 576r2
154 + 768r + 576r2 = -576r2 + 576r2

Combine like terms: -576r2 + 576r2 = 0
154 + 768r + 576r2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(77 + 384r + 288r2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(77 + 384r + 288r2)' equal to zero and attempt to solve:

Simplifying
77 + 384r + 288r2 = 0

Solving
77 + 384r + 288r2 = 0

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

Divide each side by '288'.
0.2673611111 + 1.333333333r + r2 = 0

Move the constant term to the right:

Add '-0.2673611111' to each side of the equation.
0.2673611111 + 1.333333333r + -0.2673611111 + r2 = 0 + -0.2673611111

Reorder the terms:
0.2673611111 + -0.2673611111 + 1.333333333r + r2 = 0 + -0.2673611111

Combine like terms: 0.2673611111 + -0.2673611111 = 0.0000000000
0.0000000000 + 1.333333333r + r2 = 0 + -0.2673611111
1.333333333r + r2 = 0 + -0.2673611111

Combine like terms: 0 + -0.2673611111 = -0.2673611111
1.333333333r + r2 = -0.2673611111

The r term is 1.333333333r.  Take half its coefficient (0.6666666665).
Square it (0.4444444442) and add it to both sides.

Add '0.4444444442' to each side of the equation.
1.333333333r + 0.4444444442 + r2 = -0.2673611111 + 0.4444444442

Reorder the terms:
0.4444444442 + 1.333333333r + r2 = -0.2673611111 + 0.4444444442

Combine like terms: -0.2673611111 + 0.4444444442 = 0.1770833331
0.4444444442 + 1.333333333r + r2 = 0.1770833331

Factor a perfect square on the left side:
(r + 0.6666666665)(r + 0.6666666665) = 0.1770833331

Calculate the square root of the right side: 0.420812705

Break this problem into two subproblems by setting 
(r + 0.6666666665) equal to 0.420812705 and -0.420812705.

Subproblem 1
r + 0.6666666665 = 0.420812705

Simplifying
r + 0.6666666665 = 0.420812705

Reorder the terms:
0.6666666665 + r = 0.420812705

Solving
0.6666666665 + r = 0.420812705

Solving for variable 'r'.

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

Add '-0.6666666665' to each side of the equation.
0.6666666665 + -0.6666666665 + r = 0.420812705 + -0.6666666665

Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000
0.0000000000 + r = 0.420812705 + -0.6666666665
r = 0.420812705 + -0.6666666665

Combine like terms: 0.420812705 + -0.6666666665 = -0.2458539615
r = -0.2458539615

Simplifying
r = -0.2458539615

Subproblem 2
r + 0.6666666665 = -0.420812705

Simplifying
r + 0.6666666665 = -0.420812705

Reorder the terms:
0.6666666665 + r = -0.420812705

Solving
0.6666666665 + r = -0.420812705

Solving for variable 'r'.

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

Add '-0.6666666665' to each side of the equation.
0.6666666665 + -0.6666666665 + r = -0.420812705 + -0.6666666665

Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000
0.0000000000 + r = -0.420812705 + -0.6666666665
r = -0.420812705 + -0.6666666665

Combine like terms: -0.420812705 + -0.6666666665 = -1.0874793715
r = -1.0874793715

Simplifying
r = -1.0874793715

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {-0.2458539615, -1.0874793715}
Solution
r = {-0.2458539615, -1.0874793715}