(2x-1)(2x+1)+6=4(x-4)+3x

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Solution for (2x-1)(2x+1)+6=4(x-4)+3x equation:


Simplifying
(2x + -1)(2x + 1) + 6 = 4(x + -4) + 3x

Reorder the terms:
(-1 + 2x)(2x + 1) + 6 = 4(x + -4) + 3x

Reorder the terms:
(-1 + 2x)(1 + 2x) + 6 = 4(x + -4) + 3x

Multiply (-1 + 2x) * (1 + 2x)
(-1(1 + 2x) + 2x * (1 + 2x)) + 6 = 4(x + -4) + 3x
((1 * -1 + 2x * -1) + 2x * (1 + 2x)) + 6 = 4(x + -4) + 3x
((-1 + -2x) + 2x * (1 + 2x)) + 6 = 4(x + -4) + 3x
(-1 + -2x + (1 * 2x + 2x * 2x)) + 6 = 4(x + -4) + 3x
(-1 + -2x + (2x + 4x2)) + 6 = 4(x + -4) + 3x

Combine like terms: -2x + 2x = 0
(-1 + 0 + 4x2) + 6 = 4(x + -4) + 3x
(-1 + 4x2) + 6 = 4(x + -4) + 3x

Reorder the terms:
-1 + 6 + 4x2 = 4(x + -4) + 3x

Combine like terms: -1 + 6 = 5
5 + 4x2 = 4(x + -4) + 3x

Reorder the terms:
5 + 4x2 = 4(-4 + x) + 3x
5 + 4x2 = (-4 * 4 + x * 4) + 3x
5 + 4x2 = (-16 + 4x) + 3x

Combine like terms: 4x + 3x = 7x
5 + 4x2 = -16 + 7x

Solving
5 + 4x2 = -16 + 7x

Solving for variable 'x'.

Reorder the terms:
5 + 16 + -7x + 4x2 = -16 + 7x + 16 + -7x

Combine like terms: 5 + 16 = 21
21 + -7x + 4x2 = -16 + 7x + 16 + -7x

Reorder the terms:
21 + -7x + 4x2 = -16 + 16 + 7x + -7x

Combine like terms: -16 + 16 = 0
21 + -7x + 4x2 = 0 + 7x + -7x
21 + -7x + 4x2 = 7x + -7x

Combine like terms: 7x + -7x = 0
21 + -7x + 4x2 = 0

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

Divide each side by '4'.
5.25 + -1.75x + x2 = 0

Move the constant term to the right:

Add '-5.25' to each side of the equation.
5.25 + -1.75x + -5.25 + x2 = 0 + -5.25

Reorder the terms:
5.25 + -5.25 + -1.75x + x2 = 0 + -5.25

Combine like terms: 5.25 + -5.25 = 0.00
0.00 + -1.75x + x2 = 0 + -5.25
-1.75x + x2 = 0 + -5.25

Combine like terms: 0 + -5.25 = -5.25
-1.75x + x2 = -5.25

The x term is -1.75x.  Take half its coefficient (-0.875).
Square it (0.765625) and add it to both sides.

Add '0.765625' to each side of the equation.
-1.75x + 0.765625 + x2 = -5.25 + 0.765625

Reorder the terms:
0.765625 + -1.75x + x2 = -5.25 + 0.765625

Combine like terms: -5.25 + 0.765625 = -4.484375
0.765625 + -1.75x + x2 = -4.484375

Factor a perfect square on the left side:
(x + -0.875)(x + -0.875) = -4.484375

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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