6x(4x+3)=92

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Solution for 6x(4x+3)=92 equation:


Simplifying
6x(4x + 3) = 92

Reorder the terms:
6x(3 + 4x) = 92
(3 * 6x + 4x * 6x) = 92
(18x + 24x2) = 92

Solving
18x + 24x2 = 92

Solving for variable 'x'.

Reorder the terms:
-92 + 18x + 24x2 = 92 + -92

Combine like terms: 92 + -92 = 0
-92 + 18x + 24x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-46 + 9x + 12x2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-46 + 9x + 12x2)' equal to zero and attempt to solve: Simplifying -46 + 9x + 12x2 = 0 Solving -46 + 9x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -3.833333333 + 0.75x + x2 = 0 Move the constant term to the right: Add '3.833333333' to each side of the equation. -3.833333333 + 0.75x + 3.833333333 + x2 = 0 + 3.833333333 Reorder the terms: -3.833333333 + 3.833333333 + 0.75x + x2 = 0 + 3.833333333 Combine like terms: -3.833333333 + 3.833333333 = 0.000000000 0.000000000 + 0.75x + x2 = 0 + 3.833333333 0.75x + x2 = 0 + 3.833333333 Combine like terms: 0 + 3.833333333 = 3.833333333 0.75x + x2 = 3.833333333 The x term is 0.75x. Take half its coefficient (0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. 0.75x + 0.140625 + x2 = 3.833333333 + 0.140625 Reorder the terms: 0.140625 + 0.75x + x2 = 3.833333333 + 0.140625 Combine like terms: 3.833333333 + 0.140625 = 3.973958333 0.140625 + 0.75x + x2 = 3.973958333 Factor a perfect square on the left side: (x + 0.375)(x + 0.375) = 3.973958333 Calculate the square root of the right side: 1.993478952 Break this problem into two subproblems by setting (x + 0.375) equal to 1.993478952 and -1.993478952.

Subproblem 1

x + 0.375 = 1.993478952 Simplifying x + 0.375 = 1.993478952 Reorder the terms: 0.375 + x = 1.993478952 Solving 0.375 + x = 1.993478952 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + x = 1.993478952 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = 1.993478952 + -0.375 x = 1.993478952 + -0.375 Combine like terms: 1.993478952 + -0.375 = 1.618478952 x = 1.618478952 Simplifying x = 1.618478952

Subproblem 2

x + 0.375 = -1.993478952 Simplifying x + 0.375 = -1.993478952 Reorder the terms: 0.375 + x = -1.993478952 Solving 0.375 + x = -1.993478952 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + x = -1.993478952 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = -1.993478952 + -0.375 x = -1.993478952 + -0.375 Combine like terms: -1.993478952 + -0.375 = -2.368478952 x = -2.368478952 Simplifying x = -2.368478952

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.618478952, -2.368478952}

Solution

x = {1.618478952, -2.368478952}

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