(6x)(12x+5)=95

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Solution for (6x)(12x+5)=95 equation:


Simplifying
(6x)(12x + 5) = 95

Remove parenthesis around (6x)
6x(12x + 5) = 95

Reorder the terms:
6x(5 + 12x) = 95
(5 * 6x + 12x * 6x) = 95
(30x + 72x2) = 95

Solving
30x + 72x2 = 95

Solving for variable 'x'.

Reorder the terms:
-95 + 30x + 72x2 = 95 + -95

Combine like terms: 95 + -95 = 0
-95 + 30x + 72x2 = 0

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

Divide each side by '72'.
-1.319444444 + 0.4166666667x + x2 = 0

Move the constant term to the right:

Add '1.319444444' to each side of the equation.
-1.319444444 + 0.4166666667x + 1.319444444 + x2 = 0 + 1.319444444

Reorder the terms:
-1.319444444 + 1.319444444 + 0.4166666667x + x2 = 0 + 1.319444444

Combine like terms: -1.319444444 + 1.319444444 = 0.000000000
0.000000000 + 0.4166666667x + x2 = 0 + 1.319444444
0.4166666667x + x2 = 0 + 1.319444444

Combine like terms: 0 + 1.319444444 = 1.319444444
0.4166666667x + x2 = 1.319444444

The x term is 0.4166666667x.  Take half its coefficient (0.2083333334).
Square it (0.04340277781) and add it to both sides.

Add '0.04340277781' to each side of the equation.
0.4166666667x + 0.04340277781 + x2 = 1.319444444 + 0.04340277781

Reorder the terms:
0.04340277781 + 0.4166666667x + x2 = 1.319444444 + 0.04340277781

Combine like terms: 1.319444444 + 0.04340277781 = 1.36284722181
0.04340277781 + 0.4166666667x + x2 = 1.36284722181

Factor a perfect square on the left side:
(x + 0.2083333334)(x + 0.2083333334) = 1.36284722181

Calculate the square root of the right side: 1.167410477

Break this problem into two subproblems by setting 
(x + 0.2083333334) equal to 1.167410477 and -1.167410477.

Subproblem 1

x + 0.2083333334 = 1.167410477 Simplifying x + 0.2083333334 = 1.167410477 Reorder the terms: 0.2083333334 + x = 1.167410477 Solving 0.2083333334 + x = 1.167410477 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2083333334' to each side of the equation. 0.2083333334 + -0.2083333334 + x = 1.167410477 + -0.2083333334 Combine like terms: 0.2083333334 + -0.2083333334 = 0.0000000000 0.0000000000 + x = 1.167410477 + -0.2083333334 x = 1.167410477 + -0.2083333334 Combine like terms: 1.167410477 + -0.2083333334 = 0.9590771436 x = 0.9590771436 Simplifying x = 0.9590771436

Subproblem 2

x + 0.2083333334 = -1.167410477 Simplifying x + 0.2083333334 = -1.167410477 Reorder the terms: 0.2083333334 + x = -1.167410477 Solving 0.2083333334 + x = -1.167410477 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2083333334' to each side of the equation. 0.2083333334 + -0.2083333334 + x = -1.167410477 + -0.2083333334 Combine like terms: 0.2083333334 + -0.2083333334 = 0.0000000000 0.0000000000 + x = -1.167410477 + -0.2083333334 x = -1.167410477 + -0.2083333334 Combine like terms: -1.167410477 + -0.2083333334 = -1.3757438104 x = -1.3757438104 Simplifying x = -1.3757438104

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.9590771436, -1.3757438104}

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