(x+6)(4x-3)=(2x+3)2

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Solution for (x+6)(4x-3)=(2x+3)2 equation:


Simplifying
(x + 6)(4x + -3) = (2x + 3) * 2

Reorder the terms:
(6 + x)(4x + -3) = (2x + 3) * 2

Reorder the terms:
(6 + x)(-3 + 4x) = (2x + 3) * 2

Multiply (6 + x) * (-3 + 4x)
(6(-3 + 4x) + x(-3 + 4x)) = (2x + 3) * 2
((-3 * 6 + 4x * 6) + x(-3 + 4x)) = (2x + 3) * 2
((-18 + 24x) + x(-3 + 4x)) = (2x + 3) * 2
(-18 + 24x + (-3 * x + 4x * x)) = (2x + 3) * 2
(-18 + 24x + (-3x + 4x2)) = (2x + 3) * 2

Combine like terms: 24x + -3x = 21x
(-18 + 21x + 4x2) = (2x + 3) * 2

Reorder the terms:
-18 + 21x + 4x2 = (3 + 2x) * 2

Reorder the terms for easier multiplication:
-18 + 21x + 4x2 = 2(3 + 2x)
-18 + 21x + 4x2 = (3 * 2 + 2x * 2)
-18 + 21x + 4x2 = (6 + 4x)

Solving
-18 + 21x + 4x2 = 6 + 4x

Solving for variable 'x'.

Reorder the terms:
-18 + -6 + 21x + -4x + 4x2 = 6 + 4x + -6 + -4x

Combine like terms: -18 + -6 = -24
-24 + 21x + -4x + 4x2 = 6 + 4x + -6 + -4x

Combine like terms: 21x + -4x = 17x
-24 + 17x + 4x2 = 6 + 4x + -6 + -4x

Reorder the terms:
-24 + 17x + 4x2 = 6 + -6 + 4x + -4x

Combine like terms: 6 + -6 = 0
-24 + 17x + 4x2 = 0 + 4x + -4x
-24 + 17x + 4x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
-24 + 17x + 4x2 = 0

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

Divide each side by '4'.
-6 + 4.25x + x2 = 0

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + 4.25x + 6 + x2 = 0 + 6

Reorder the terms:
-6 + 6 + 4.25x + x2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + 4.25x + x2 = 0 + 6
4.25x + x2 = 0 + 6

Combine like terms: 0 + 6 = 6
4.25x + x2 = 6

The x term is 4.25x.  Take half its coefficient (2.125).
Square it (4.515625) and add it to both sides.

Add '4.515625' to each side of the equation.
4.25x + 4.515625 + x2 = 6 + 4.515625

Reorder the terms:
4.515625 + 4.25x + x2 = 6 + 4.515625

Combine like terms: 6 + 4.515625 = 10.515625
4.515625 + 4.25x + x2 = 10.515625

Factor a perfect square on the left side:
(x + 2.125)(x + 2.125) = 10.515625

Calculate the square root of the right side: 3.242780443

Break this problem into two subproblems by setting 
(x + 2.125) equal to 3.242780443 and -3.242780443.

Subproblem 1

x + 2.125 = 3.242780443 Simplifying x + 2.125 = 3.242780443 Reorder the terms: 2.125 + x = 3.242780443 Solving 2.125 + x = 3.242780443 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.125' to each side of the equation. 2.125 + -2.125 + x = 3.242780443 + -2.125 Combine like terms: 2.125 + -2.125 = 0.000 0.000 + x = 3.242780443 + -2.125 x = 3.242780443 + -2.125 Combine like terms: 3.242780443 + -2.125 = 1.117780443 x = 1.117780443 Simplifying x = 1.117780443

Subproblem 2

x + 2.125 = -3.242780443 Simplifying x + 2.125 = -3.242780443 Reorder the terms: 2.125 + x = -3.242780443 Solving 2.125 + x = -3.242780443 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.125' to each side of the equation. 2.125 + -2.125 + x = -3.242780443 + -2.125 Combine like terms: 2.125 + -2.125 = 0.000 0.000 + x = -3.242780443 + -2.125 x = -3.242780443 + -2.125 Combine like terms: -3.242780443 + -2.125 = -5.367780443 x = -5.367780443 Simplifying x = -5.367780443

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.117780443, -5.367780443}

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