(8x+26)(3x)=180

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Solution for (8x+26)(3x)=180 equation: 


Simplifying
(8x + 26)(3x) = 180

Reorder the terms:
(26 + 8x)(3x) = 180

Remove parenthesis around (3x)
(26 + 8x) * 3x = 180

Reorder the terms for easier multiplication:
3x(26 + 8x) = 180
(26 * 3x + 8x * 3x) = 180
(78x + 24x2) = 180

Solving
78x + 24x2 = 180

Solving for variable 'x'.

Reorder the terms:
-180 + 78x + 24x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-180 + 78x + 24x2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-30 + 13x + 4x2) = 0

Ignore the factor 6.

Subproblem 1
Set the factor '(-30 + 13x + 4x2)' equal to zero and attempt to solve:

Simplifying
-30 + 13x + 4x2 = 0

Solving
-30 + 13x + 4x2 = 0

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

Divide each side by '4'.
-7.5 + 3.25x + x2 = 0

Move the constant term to the right:

Add '7.5' to each side of the equation.
-7.5 + 3.25x + 7.5 + x2 = 0 + 7.5

Reorder the terms:
-7.5 + 7.5 + 3.25x + x2 = 0 + 7.5

Combine like terms: -7.5 + 7.5 = 0.0
0.0 + 3.25x + x2 = 0 + 7.5
3.25x + x2 = 0 + 7.5

Combine like terms: 0 + 7.5 = 7.5
3.25x + x2 = 7.5

The x term is 3.25x.  Take half its coefficient (1.625).
Square it (2.640625) and add it to both sides.

Add '2.640625' to each side of the equation.
3.25x + 2.640625 + x2 = 7.5 + 2.640625

Reorder the terms:
2.640625 + 3.25x + x2 = 7.5 + 2.640625

Combine like terms: 7.5 + 2.640625 = 10.140625
2.640625 + 3.25x + x2 = 10.140625

Factor a perfect square on the left side:
(x + 1.625)(x + 1.625) = 10.140625

Calculate the square root of the right side: 3.184434801

Break this problem into two subproblems by setting 
(x + 1.625) equal to 3.184434801 and -3.184434801.


Subproblem 1
x + 1.625 = 3.184434801

Simplifying
x + 1.625 = 3.184434801

Reorder the terms:
1.625 + x = 3.184434801

Solving
1.625 + x = 3.184434801

Solving for variable 'x'.

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

Add '-1.625' to each side of the equation.
1.625 + -1.625 + x = 3.184434801 + -1.625

Combine like terms: 1.625 + -1.625 = 0.000
0.000 + x = 3.184434801 + -1.625
x = 3.184434801 + -1.625

Combine like terms: 3.184434801 + -1.625 = 1.559434801
x = 1.559434801

Simplifying
x = 1.559434801


Subproblem 2
x + 1.625 = -3.184434801

Simplifying
x + 1.625 = -3.184434801

Reorder the terms:
1.625 + x = -3.184434801

Solving
1.625 + x = -3.184434801

Solving for variable 'x'.

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

Add '-1.625' to each side of the equation.
1.625 + -1.625 + x = -3.184434801 + -1.625

Combine like terms: 1.625 + -1.625 = 0.000
0.000 + x = -3.184434801 + -1.625
x = -3.184434801 + -1.625

Combine like terms: -3.184434801 + -1.625 = -4.809434801
x = -4.809434801

Simplifying
x = -4.809434801


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.559434801, -4.809434801}
Solution
x = {1.559434801, -4.809434801}

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