(4x-1)(x+3)=(4x)2-7

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Solution for (4x-1)(x+3)=(4x)2-7 equation:


Simplifying
(4x + -1)(x + 3) = (4x) * 2 + -7

Reorder the terms:
(-1 + 4x)(x + 3) = (4x) * 2 + -7

Reorder the terms:
(-1 + 4x)(3 + x) = (4x) * 2 + -7

Multiply (-1 + 4x) * (3 + x)
(-1(3 + x) + 4x * (3 + x)) = (4x) * 2 + -7
((3 * -1 + x * -1) + 4x * (3 + x)) = (4x) * 2 + -7
((-3 + -1x) + 4x * (3 + x)) = (4x) * 2 + -7
(-3 + -1x + (3 * 4x + x * 4x)) = (4x) * 2 + -7
(-3 + -1x + (12x + 4x2)) = (4x) * 2 + -7

Combine like terms: -1x + 12x = 11x
(-3 + 11x + 4x2) = (4x) * 2 + -7

Remove parenthesis around (4x)
-3 + 11x + 4x2 = 4x * 2 + -7

Reorder the terms for easier multiplication:
-3 + 11x + 4x2 = 4 * 2x + -7

Multiply 4 * 2
-3 + 11x + 4x2 = 8x + -7

Reorder the terms:
-3 + 11x + 4x2 = -7 + 8x

Solving
-3 + 11x + 4x2 = -7 + 8x

Solving for variable 'x'.

Reorder the terms:
-3 + 7 + 11x + -8x + 4x2 = -7 + 8x + 7 + -8x

Combine like terms: -3 + 7 = 4
4 + 11x + -8x + 4x2 = -7 + 8x + 7 + -8x

Combine like terms: 11x + -8x = 3x
4 + 3x + 4x2 = -7 + 8x + 7 + -8x

Reorder the terms:
4 + 3x + 4x2 = -7 + 7 + 8x + -8x

Combine like terms: -7 + 7 = 0
4 + 3x + 4x2 = 0 + 8x + -8x
4 + 3x + 4x2 = 8x + -8x

Combine like terms: 8x + -8x = 0
4 + 3x + 4x2 = 0

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

Divide each side by '4'.
1 + 0.75x + x2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + 0.75x + -1 + x2 = 0 + -1

Reorder the terms:
1 + -1 + 0.75x + x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 0.75x + x2 = 0 + -1
0.75x + x2 = 0 + -1

Combine like terms: 0 + -1 = -1
0.75x + x2 = -1

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 = -1 + 0.140625

Reorder the terms:
0.140625 + 0.75x + x2 = -1 + 0.140625

Combine like terms: -1 + 0.140625 = -0.859375
0.140625 + 0.75x + x2 = -0.859375

Factor a perfect square on the left side:
(x + 0.375)(x + 0.375) = -0.859375

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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