(x+3)(4x-1)=27

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Solution for (x+3)(4x-1)=27 equation:


Simplifying
(x + 3)(4x + -1) = 27

Reorder the terms:
(3 + x)(4x + -1) = 27

Reorder the terms:
(3 + x)(-1 + 4x) = 27

Multiply (3 + x) * (-1 + 4x)
(3(-1 + 4x) + x(-1 + 4x)) = 27
((-1 * 3 + 4x * 3) + x(-1 + 4x)) = 27
((-3 + 12x) + x(-1 + 4x)) = 27
(-3 + 12x + (-1 * x + 4x * x)) = 27
(-3 + 12x + (-1x + 4x2)) = 27

Combine like terms: 12x + -1x = 11x
(-3 + 11x + 4x2) = 27

Solving
-3 + 11x + 4x2 = 27

Solving for variable 'x'.

Reorder the terms:
-3 + -27 + 11x + 4x2 = 27 + -27

Combine like terms: -3 + -27 = -30
-30 + 11x + 4x2 = 27 + -27

Combine like terms: 27 + -27 = 0
-30 + 11x + 4x2 = 0

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

Divide each side by '4'.
-7.5 + 2.75x + x2 = 0

Move the constant term to the right:

Add '7.5' to each side of the equation.
-7.5 + 2.75x + 7.5 + x2 = 0 + 7.5

Reorder the terms:
-7.5 + 7.5 + 2.75x + x2 = 0 + 7.5

Combine like terms: -7.5 + 7.5 = 0.0
0.0 + 2.75x + x2 = 0 + 7.5
2.75x + x2 = 0 + 7.5

Combine like terms: 0 + 7.5 = 7.5
2.75x + x2 = 7.5

The x term is 2.75x.  Take half its coefficient (1.375).
Square it (1.890625) and add it to both sides.

Add '1.890625' to each side of the equation.
2.75x + 1.890625 + x2 = 7.5 + 1.890625

Reorder the terms:
1.890625 + 2.75x + x2 = 7.5 + 1.890625

Combine like terms: 7.5 + 1.890625 = 9.390625
1.890625 + 2.75x + x2 = 9.390625

Factor a perfect square on the left side:
(x + 1.375)(x + 1.375) = 9.390625

Calculate the square root of the right side: 3.064412668

Break this problem into two subproblems by setting 
(x + 1.375) equal to 3.064412668 and -3.064412668.

Subproblem 1

x + 1.375 = 3.064412668 Simplifying x + 1.375 = 3.064412668 Reorder the terms: 1.375 + x = 3.064412668 Solving 1.375 + x = 3.064412668 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.375' to each side of the equation. 1.375 + -1.375 + x = 3.064412668 + -1.375 Combine like terms: 1.375 + -1.375 = 0.000 0.000 + x = 3.064412668 + -1.375 x = 3.064412668 + -1.375 Combine like terms: 3.064412668 + -1.375 = 1.689412668 x = 1.689412668 Simplifying x = 1.689412668

Subproblem 2

x + 1.375 = -3.064412668 Simplifying x + 1.375 = -3.064412668 Reorder the terms: 1.375 + x = -3.064412668 Solving 1.375 + x = -3.064412668 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.375' to each side of the equation. 1.375 + -1.375 + x = -3.064412668 + -1.375 Combine like terms: 1.375 + -1.375 = 0.000 0.000 + x = -3.064412668 + -1.375 x = -3.064412668 + -1.375 Combine like terms: -3.064412668 + -1.375 = -4.439412668 x = -4.439412668 Simplifying x = -4.439412668

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.689412668, -4.439412668}

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