3x(4x+5)+6x=20

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Solution for 3x(4x+5)+6x=20 equation: 


Simplifying
3x(4x + 5) + 6x = 20

Reorder the terms:
3x(5 + 4x) + 6x = 20
(5 * 3x + 4x * 3x) + 6x = 20
(15x + 12x2) + 6x = 20

Reorder the terms:
15x + 6x + 12x2 = 20

Combine like terms: 15x + 6x = 21x
21x + 12x2 = 20

Solving
21x + 12x2 = 20

Solving for variable 'x'.

Reorder the terms:
-20 + 21x + 12x2 = 20 + -20

Combine like terms: 20 + -20 = 0
-20 + 21x + 12x2 = 0

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

Divide each side by '12'.
-1.666666667 + 1.75x + x2 = 0

Move the constant term to the right:

Add '1.666666667' to each side of the equation.
-1.666666667 + 1.75x + 1.666666667 + x2 = 0 + 1.666666667

Reorder the terms:
-1.666666667 + 1.666666667 + 1.75x + x2 = 0 + 1.666666667

Combine like terms: -1.666666667 + 1.666666667 = 0.000000000
0.000000000 + 1.75x + x2 = 0 + 1.666666667
1.75x + x2 = 0 + 1.666666667

Combine like terms: 0 + 1.666666667 = 1.666666667
1.75x + x2 = 1.666666667

The x term is 1.75x.  Take half its coefficient (0.875).
Square it (0.765625) and add it to both sides.

Add '0.765625' to each side of the equation.
1.75x + 0.765625 + x2 = 1.666666667 + 0.765625

Reorder the terms:
0.765625 + 1.75x + x2 = 1.666666667 + 0.765625

Combine like terms: 1.666666667 + 0.765625 = 2.432291667
0.765625 + 1.75x + x2 = 2.432291667

Factor a perfect square on the left side:
(x + 0.875)(x + 0.875) = 2.432291667

Calculate the square root of the right side: 1.559580606

Break this problem into two subproblems by setting 
(x + 0.875) equal to 1.559580606 and -1.559580606.


Subproblem 1
x + 0.875 = 1.559580606

Simplifying
x + 0.875 = 1.559580606

Reorder the terms:
0.875 + x = 1.559580606

Solving
0.875 + x = 1.559580606

Solving for variable 'x'.

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

Add '-0.875' to each side of the equation.
0.875 + -0.875 + x = 1.559580606 + -0.875

Combine like terms: 0.875 + -0.875 = 0.000
0.000 + x = 1.559580606 + -0.875
x = 1.559580606 + -0.875

Combine like terms: 1.559580606 + -0.875 = 0.684580606
x = 0.684580606

Simplifying
x = 0.684580606


Subproblem 2
x + 0.875 = -1.559580606

Simplifying
x + 0.875 = -1.559580606

Reorder the terms:
0.875 + x = -1.559580606

Solving
0.875 + x = -1.559580606

Solving for variable 'x'.

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

Add '-0.875' to each side of the equation.
0.875 + -0.875 + x = -1.559580606 + -0.875

Combine like terms: 0.875 + -0.875 = 0.000
0.000 + x = -1.559580606 + -0.875
x = -1.559580606 + -0.875

Combine like terms: -1.559580606 + -0.875 = -2.434580606
x = -2.434580606

Simplifying
x = -2.434580606


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.684580606, -2.434580606}

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