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

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

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

Reorder the terms:
3(-1 + 4x) + (2x + -1)(2x + -1) = -7
(-1 * 3 + 4x * 3) + (2x + -1)(2x + -1) = -7
(-3 + 12x) + (2x + -1)(2x + -1) = -7

Reorder the terms:
-3 + 12x + (-1 + 2x)(2x + -1) = -7

Reorder the terms:
-3 + 12x + (-1 + 2x)(-1 + 2x) = -7

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

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

Reorder the terms:
-3 + 1 + 12x + -4x + 4x2 = -7

Combine like terms: -3 + 1 = -2
-2 + 12x + -4x + 4x2 = -7

Combine like terms: 12x + -4x = 8x
-2 + 8x + 4x2 = -7

Solving
-2 + 8x + 4x2 = -7

Solving for variable 'x'.

Reorder the terms:
-2 + 7 + 8x + 4x2 = -7 + 7

Combine like terms: -2 + 7 = 5
5 + 8x + 4x2 = -7 + 7

Combine like terms: -7 + 7 = 0
5 + 8x + 4x2 = 0

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

Divide each side by '4'.
1.25 + 2x + x2 = 0

Move the constant term to the right:

Add '-1.25' to each side of the equation.
1.25 + 2x + -1.25 + x2 = 0 + -1.25

Reorder the terms:
1.25 + -1.25 + 2x + x2 = 0 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + 2x + x2 = 0 + -1.25
2x + x2 = 0 + -1.25

Combine like terms: 0 + -1.25 = -1.25
2x + x2 = -1.25

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = -1.25 + 1

Reorder the terms:
1 + 2x + x2 = -1.25 + 1

Combine like terms: -1.25 + 1 = -0.25
1 + 2x + x2 = -0.25

Factor a perfect square on the left side:
(x + 1)(x + 1) = -0.25

Can't calculate square root of the right side.

The solution to this equation could not be determined.