3=(4x+1)(x-7)

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Solution for 3=(4x+1)(x-7) equation:


Simplifying
3 = (4x + 1)(x + -7)

Reorder the terms:
3 = (1 + 4x)(x + -7)

Reorder the terms:
3 = (1 + 4x)(-7 + x)

Multiply (1 + 4x) * (-7 + x)
3 = (1(-7 + x) + 4x * (-7 + x))
3 = ((-7 * 1 + x * 1) + 4x * (-7 + x))
3 = ((-7 + 1x) + 4x * (-7 + x))
3 = (-7 + 1x + (-7 * 4x + x * 4x))
3 = (-7 + 1x + (-28x + 4x2))

Combine like terms: 1x + -28x = -27x
3 = (-7 + -27x + 4x2)

Solving
3 = -7 + -27x + 4x2

Solving for variable 'x'.

Combine like terms: 3 + 7 = 10
10 + 27x + -4x2 = -7 + -27x + 4x2 + 7 + 27x + -4x2

Reorder the terms:
10 + 27x + -4x2 = -7 + 7 + -27x + 27x + 4x2 + -4x2

Combine like terms: -7 + 7 = 0
10 + 27x + -4x2 = 0 + -27x + 27x + 4x2 + -4x2
10 + 27x + -4x2 = -27x + 27x + 4x2 + -4x2

Combine like terms: -27x + 27x = 0
10 + 27x + -4x2 = 0 + 4x2 + -4x2
10 + 27x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
10 + 27x + -4x2 = 0

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

Divide each side by '-4'.
-2.5 + -6.75x + x2 = 0

Move the constant term to the right:

Add '2.5' to each side of the equation.
-2.5 + -6.75x + 2.5 + x2 = 0 + 2.5

Reorder the terms:
-2.5 + 2.5 + -6.75x + x2 = 0 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + -6.75x + x2 = 0 + 2.5
-6.75x + x2 = 0 + 2.5

Combine like terms: 0 + 2.5 = 2.5
-6.75x + x2 = 2.5

The x term is -6.75x.  Take half its coefficient (-3.375).
Square it (11.390625) and add it to both sides.

Add '11.390625' to each side of the equation.
-6.75x + 11.390625 + x2 = 2.5 + 11.390625

Reorder the terms:
11.390625 + -6.75x + x2 = 2.5 + 11.390625

Combine like terms: 2.5 + 11.390625 = 13.890625
11.390625 + -6.75x + x2 = 13.890625

Factor a perfect square on the left side:
(x + -3.375)(x + -3.375) = 13.890625

Calculate the square root of the right side: 3.727012879

Break this problem into two subproblems by setting 
(x + -3.375) equal to 3.727012879 and -3.727012879.

Subproblem 1

x + -3.375 = 3.727012879 Simplifying x + -3.375 = 3.727012879 Reorder the terms: -3.375 + x = 3.727012879 Solving -3.375 + x = 3.727012879 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.375' to each side of the equation. -3.375 + 3.375 + x = 3.727012879 + 3.375 Combine like terms: -3.375 + 3.375 = 0.000 0.000 + x = 3.727012879 + 3.375 x = 3.727012879 + 3.375 Combine like terms: 3.727012879 + 3.375 = 7.102012879 x = 7.102012879 Simplifying x = 7.102012879

Subproblem 2

x + -3.375 = -3.727012879 Simplifying x + -3.375 = -3.727012879 Reorder the terms: -3.375 + x = -3.727012879 Solving -3.375 + x = -3.727012879 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.375' to each side of the equation. -3.375 + 3.375 + x = -3.727012879 + 3.375 Combine like terms: -3.375 + 3.375 = 0.000 0.000 + x = -3.727012879 + 3.375 x = -3.727012879 + 3.375 Combine like terms: -3.727012879 + 3.375 = -0.352012879 x = -0.352012879 Simplifying x = -0.352012879

Solution

The solution to the problem is based on the solutions from the subproblems. x = {7.102012879, -0.352012879}

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