2x(x+2)-3(x-1)+8=3x-1

Solution for 2x(x+2)-3(x-1)+8=3x-1 equation:

Simplifying
2x(x + 2) + -3(x + -1) + 8 = 3x + -1

Reorder the terms:
2x(2 + x) + -3(x + -1) + 8 = 3x + -1
(2 * 2x + x * 2x) + -3(x + -1) + 8 = 3x + -1
(4x + 2x2) + -3(x + -1) + 8 = 3x + -1

Reorder the terms:
4x + 2x2 + -3(-1 + x) + 8 = 3x + -1
4x + 2x2 + (-1 * -3 + x * -3) + 8 = 3x + -1
4x + 2x2 + (3 + -3x) + 8 = 3x + -1

Reorder the terms:
3 + 8 + 4x + -3x + 2x2 = 3x + -1

Combine like terms: 3 + 8 = 11
11 + 4x + -3x + 2x2 = 3x + -1

Combine like terms: 4x + -3x = 1x
11 + 1x + 2x2 = 3x + -1

Reorder the terms:
11 + 1x + 2x2 = -1 + 3x

Solving
11 + 1x + 2x2 = -1 + 3x

Solving for variable 'x'.

Reorder the terms:
11 + 1 + 1x + -3x + 2x2 = -1 + 3x + 1 + -3x

Combine like terms: 11 + 1 = 12
12 + 1x + -3x + 2x2 = -1 + 3x + 1 + -3x

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

Reorder the terms:
12 + -2x + 2x2 = -1 + 1 + 3x + -3x

Combine like terms: -1 + 1 = 0
12 + -2x + 2x2 = 0 + 3x + -3x
12 + -2x + 2x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
12 + -2x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(6 + -1x + x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(6 + -1x + x2)' equal to zero and attempt to solve:

Simplifying
6 + -1x + x2 = 0

Solving
6 + -1x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-6' to each side of the equation.
6 + -1x + -6 + x2 = 0 + -6

Reorder the terms:
6 + -6 + -1x + x2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x + x2 = 0 + -6
-1x + x2 = 0 + -6

Combine like terms: 0 + -6 = -6
-1x + x2 = -6

The x term is -1x.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1x + 0.25 + x2 = -6 + 0.25

Reorder the terms:
0.25 + -1x + x2 = -6 + 0.25

Combine like terms: -6 + 0.25 = -5.75
0.25 + -1x + x2 = -5.75

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = -5.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.