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

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

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

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

Reorder the terms for easier multiplication:
2(-1 + 3x) = x(2x + 3) + 7
(-1 * 2 + 3x * 2) = x(2x + 3) + 7
(-2 + 6x) = x(2x + 3) + 7

Reorder the terms:
-2 + 6x = x(3 + 2x) + 7
-2 + 6x = (3 * x + 2x * x) + 7
-2 + 6x = (3x + 2x2) + 7

Reorder the terms:
-2 + 6x = 7 + 3x + 2x2

Solving
-2 + 6x = 7 + 3x + 2x2

Solving for variable 'x'.

Reorder the terms:
-2 + -7 + 6x + -3x + -2x2 = 7 + 3x + 2x2 + -7 + -3x + -2x2

Combine like terms: -2 + -7 = -9
-9 + 6x + -3x + -2x2 = 7 + 3x + 2x2 + -7 + -3x + -2x2

Combine like terms: 6x + -3x = 3x
-9 + 3x + -2x2 = 7 + 3x + 2x2 + -7 + -3x + -2x2

Reorder the terms:
-9 + 3x + -2x2 = 7 + -7 + 3x + -3x + 2x2 + -2x2

Combine like terms: 7 + -7 = 0
-9 + 3x + -2x2 = 0 + 3x + -3x + 2x2 + -2x2
-9 + 3x + -2x2 = 3x + -3x + 2x2 + -2x2

Combine like terms: 3x + -3x = 0
-9 + 3x + -2x2 = 0 + 2x2 + -2x2
-9 + 3x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-9 + 3x + -2x2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
4.5 + -1.5x + x2 = 0

Move the constant term to the right:

Add '-4.5' to each side of the equation.
4.5 + -1.5x + -4.5 + x2 = 0 + -4.5

Reorder the terms:
4.5 + -4.5 + -1.5x + x2 = 0 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + -1.5x + x2 = 0 + -4.5
-1.5x + x2 = 0 + -4.5

Combine like terms: 0 + -4.5 = -4.5
-1.5x + x2 = -4.5

The x term is -1.5x.  Take half its coefficient (-0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
-1.5x + 0.5625 + x2 = -4.5 + 0.5625

Reorder the terms:
0.5625 + -1.5x + x2 = -4.5 + 0.5625

Combine like terms: -4.5 + 0.5625 = -3.9375
0.5625 + -1.5x + x2 = -3.9375

Factor a perfect square on the left side:
(x + -0.75)(x + -0.75) = -3.9375

Can't calculate square root of the right side.

The solution to this equation could not be determined.