6x(x-5)=4x+20

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Solution for 6x(x-5)=4x+20 equation: 


Simplifying
6x(x + -5) = 4x + 20

Reorder the terms:
6x(-5 + x) = 4x + 20
(-5 * 6x + x * 6x) = 4x + 20
(-30x + 6x2) = 4x + 20

Reorder the terms:
-30x + 6x2 = 20 + 4x

Solving
-30x + 6x2 = 20 + 4x

Solving for variable 'x'.

Reorder the terms:
-20 + -30x + -4x + 6x2 = 20 + 4x + -20 + -4x

Combine like terms: -30x + -4x = -34x
-20 + -34x + 6x2 = 20 + 4x + -20 + -4x

Reorder the terms:
-20 + -34x + 6x2 = 20 + -20 + 4x + -4x

Combine like terms: 20 + -20 = 0
-20 + -34x + 6x2 = 0 + 4x + -4x
-20 + -34x + 6x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
-20 + -34x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-10 + -17x + 3x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-10 + -17x + 3x2)' equal to zero and attempt to solve:

Simplifying
-10 + -17x + 3x2 = 0

Solving
-10 + -17x + 3x2 = 0

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

Divide each side by '3'.
-3.333333333 + -5.666666667x + x2 = 0

Move the constant term to the right:

Add '3.333333333' to each side of the equation.
-3.333333333 + -5.666666667x + 3.333333333 + x2 = 0 + 3.333333333

Reorder the terms:
-3.333333333 + 3.333333333 + -5.666666667x + x2 = 0 + 3.333333333

Combine like terms: -3.333333333 + 3.333333333 = 0.000000000
0.000000000 + -5.666666667x + x2 = 0 + 3.333333333
-5.666666667x + x2 = 0 + 3.333333333

Combine like terms: 0 + 3.333333333 = 3.333333333
-5.666666667x + x2 = 3.333333333

The x term is -5.666666667x.  Take half its coefficient (-2.833333334).
Square it (8.027777782) and add it to both sides.

Add '8.027777782' to each side of the equation.
-5.666666667x + 8.027777782 + x2 = 3.333333333 + 8.027777782

Reorder the terms:
8.027777782 + -5.666666667x + x2 = 3.333333333 + 8.027777782

Combine like terms: 3.333333333 + 8.027777782 = 11.361111115
8.027777782 + -5.666666667x + x2 = 11.361111115

Factor a perfect square on the left side:
(x + -2.833333334)(x + -2.833333334) = 11.361111115

Calculate the square root of the right side: 3.370624737

Break this problem into two subproblems by setting 
(x + -2.833333334) equal to 3.370624737 and -3.370624737.


Subproblem 1
x + -2.833333334 = 3.370624737

Simplifying
x + -2.833333334 = 3.370624737

Reorder the terms:
-2.833333334 + x = 3.370624737

Solving
-2.833333334 + x = 3.370624737

Solving for variable 'x'.

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

Add '2.833333334' to each side of the equation.
-2.833333334 + 2.833333334 + x = 3.370624737 + 2.833333334

Combine like terms: -2.833333334 + 2.833333334 = 0.000000000
0.000000000 + x = 3.370624737 + 2.833333334
x = 3.370624737 + 2.833333334

Combine like terms: 3.370624737 + 2.833333334 = 6.203958071
x = 6.203958071

Simplifying
x = 6.203958071


Subproblem 2
x + -2.833333334 = -3.370624737

Simplifying
x + -2.833333334 = -3.370624737

Reorder the terms:
-2.833333334 + x = -3.370624737

Solving
-2.833333334 + x = -3.370624737

Solving for variable 'x'.

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

Add '2.833333334' to each side of the equation.
-2.833333334 + 2.833333334 + x = -3.370624737 + 2.833333334

Combine like terms: -2.833333334 + 2.833333334 = 0.000000000
0.000000000 + x = -3.370624737 + 2.833333334
x = -3.370624737 + 2.833333334

Combine like terms: -3.370624737 + 2.833333334 = -0.537291403
x = -0.537291403

Simplifying
x = -0.537291403


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.203958071, -0.537291403}
Solution
x = {6.203958071, -0.537291403}

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