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

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

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

Reorder the terms:
3x(-4 + x) + 3 = 7 + -2(x + -1)
(-4 * 3x + x * 3x) + 3 = 7 + -2(x + -1)
(-12x + 3x2) + 3 = 7 + -2(x + -1)

Reorder the terms:
3 + -12x + 3x2 = 7 + -2(x + -1)

Reorder the terms:
3 + -12x + 3x2 = 7 + -2(-1 + x)
3 + -12x + 3x2 = 7 + (-1 * -2 + x * -2)
3 + -12x + 3x2 = 7 + (2 + -2x)

Combine like terms: 7 + 2 = 9
3 + -12x + 3x2 = 9 + -2x

Solving
3 + -12x + 3x2 = 9 + -2x

Solving for variable 'x'.

Reorder the terms:
3 + -9 + -12x + 2x + 3x2 = 9 + -2x + -9 + 2x

Combine like terms: 3 + -9 = -6
-6 + -12x + 2x + 3x2 = 9 + -2x + -9 + 2x

Combine like terms: -12x + 2x = -10x
-6 + -10x + 3x2 = 9 + -2x + -9 + 2x

Reorder the terms:
-6 + -10x + 3x2 = 9 + -9 + -2x + 2x

Combine like terms: 9 + -9 = 0
-6 + -10x + 3x2 = 0 + -2x + 2x
-6 + -10x + 3x2 = -2x + 2x

Combine like terms: -2x + 2x = 0
-6 + -10x + 3x2 = 0

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

Divide each side by '3'.
-2 + -3.333333333x + x2 = 0

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + -3.333333333x + 2 + x2 = 0 + 2

Reorder the terms:
-2 + 2 + -3.333333333x + x2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -3.333333333x + x2 = 0 + 2
-3.333333333x + x2 = 0 + 2

Combine like terms: 0 + 2 = 2
-3.333333333x + x2 = 2

The x term is -3.333333333x.  Take half its coefficient (-1.666666667).
Square it (2.777777779) and add it to both sides.

Add '2.777777779' to each side of the equation.
-3.333333333x + 2.777777779 + x2 = 2 + 2.777777779

Reorder the terms:
2.777777779 + -3.333333333x + x2 = 2 + 2.777777779

Combine like terms: 2 + 2.777777779 = 4.777777779
2.777777779 + -3.333333333x + x2 = 4.777777779

Factor a perfect square on the left side:
(x + -1.666666667)(x + -1.666666667) = 4.777777779

Calculate the square root of the right side: 2.185812842

Break this problem into two subproblems by setting 
(x + -1.666666667) equal to 2.185812842 and -2.185812842.

Subproblem 1
x + -1.666666667 = 2.185812842

Simplifying
x + -1.666666667 = 2.185812842

Reorder the terms:
-1.666666667 + x = 2.185812842

Solving
-1.666666667 + x = 2.185812842

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '1.666666667' to each side of the equation.
-1.666666667 + 1.666666667 + x = 2.185812842 + 1.666666667

Combine like terms: -1.666666667 + 1.666666667 = 0.000000000
0.000000000 + x = 2.185812842 + 1.666666667
x = 2.185812842 + 1.666666667

Combine like terms: 2.185812842 + 1.666666667 = 3.852479509
x = 3.852479509

Simplifying
x = 3.852479509

Subproblem 2
x + -1.666666667 = -2.185812842

Simplifying
x + -1.666666667 = -2.185812842

Reorder the terms:
-1.666666667 + x = -2.185812842

Solving
-1.666666667 + x = -2.185812842

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '1.666666667' to each side of the equation.
-1.666666667 + 1.666666667 + x = -2.185812842 + 1.666666667

Combine like terms: -1.666666667 + 1.666666667 = 0.000000000
0.000000000 + x = -2.185812842 + 1.666666667
x = -2.185812842 + 1.666666667

Combine like terms: -2.185812842 + 1.666666667 = -0.519146175
x = -0.519146175

Simplifying
x = -0.519146175

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.852479509, -0.519146175}