x(5x+3)+1=7(x-3)

Solution for x(5x+3)+1=7(x-3) equation:

Simplifying
x(5x + 3) + 1 = 7(x + -3)

Reorder the terms:
x(3 + 5x) + 1 = 7(x + -3)
(3 * x + 5x * x) + 1 = 7(x + -3)
(3x + 5x2) + 1 = 7(x + -3)

Reorder the terms:
1 + 3x + 5x2 = 7(x + -3)

Reorder the terms:
1 + 3x + 5x2 = 7(-3 + x)
1 + 3x + 5x2 = (-3 * 7 + x * 7)
1 + 3x + 5x2 = (-21 + 7x)

Solving
1 + 3x + 5x2 = -21 + 7x

Solving for variable 'x'.

Reorder the terms:
1 + 21 + 3x + -7x + 5x2 = -21 + 7x + 21 + -7x

Combine like terms: 1 + 21 = 22
22 + 3x + -7x + 5x2 = -21 + 7x + 21 + -7x

Combine like terms: 3x + -7x = -4x
22 + -4x + 5x2 = -21 + 7x + 21 + -7x

Reorder the terms:
22 + -4x + 5x2 = -21 + 21 + 7x + -7x

Combine like terms: -21 + 21 = 0
22 + -4x + 5x2 = 0 + 7x + -7x
22 + -4x + 5x2 = 7x + -7x

Combine like terms: 7x + -7x = 0
22 + -4x + 5x2 = 0

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

Divide each side by '5'.
4.4 + -0.8x + x2 = 0

Move the constant term to the right:

Add '-4.4' to each side of the equation.
4.4 + -0.8x + -4.4 + x2 = 0 + -4.4

Reorder the terms:
4.4 + -4.4 + -0.8x + x2 = 0 + -4.4

Combine like terms: 4.4 + -4.4 = 0.0
0.0 + -0.8x + x2 = 0 + -4.4
-0.8x + x2 = 0 + -4.4

Combine like terms: 0 + -4.4 = -4.4
-0.8x + x2 = -4.4

The x term is -0.8x.  Take half its coefficient (-0.4).
Square it (0.16) and add it to both sides.

Add '0.16' to each side of the equation.
-0.8x + 0.16 + x2 = -4.4 + 0.16

Reorder the terms:
0.16 + -0.8x + x2 = -4.4 + 0.16

Combine like terms: -4.4 + 0.16 = -4.24
0.16 + -0.8x + x2 = -4.24

Factor a perfect square on the left side:
(x + -0.4)(x + -0.4) = -4.24

Can't calculate square root of the right side.

The solution to this equation could not be determined.