7x(-13+3x)+12=13

Solution for 7x(-13+3x)+12=13 equation:

Simplifying
7x(-13 + 3x) + 12 = 13
(-13 * 7x + 3x * 7x) + 12 = 13
(-91x + 21x2) + 12 = 13

Reorder the terms:
12 + -91x + 21x2 = 13

Solving
12 + -91x + 21x2 = 13

Solving for variable 'x'.

Reorder the terms:
12 + -13 + -91x + 21x2 = 13 + -13

Combine like terms: 12 + -13 = -1
-1 + -91x + 21x2 = 13 + -13

Combine like terms: 13 + -13 = 0
-1 + -91x + 21x2 = 0

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

Divide each side by '21'.
-0.04761904762 + -4.333333333x + x2 = 0

Move the constant term to the right:

Add '0.04761904762' to each side of the equation.
-0.04761904762 + -4.333333333x + 0.04761904762 + x2 = 0 + 0.04761904762

Reorder the terms:
-0.04761904762 + 0.04761904762 + -4.333333333x + x2 = 0 + 0.04761904762

Combine like terms: -0.04761904762 + 0.04761904762 = 0.00000000000
0.00000000000 + -4.333333333x + x2 = 0 + 0.04761904762
-4.333333333x + x2 = 0 + 0.04761904762

Combine like terms: 0 + 0.04761904762 = 0.04761904762
-4.333333333x + x2 = 0.04761904762

The x term is -4.333333333x.  Take half its coefficient (-2.166666667).
Square it (4.694444446) and add it to both sides.

Add '4.694444446' to each side of the equation.
-4.333333333x + 4.694444446 + x2 = 0.04761904762 + 4.694444446

Reorder the terms:
4.694444446 + -4.333333333x + x2 = 0.04761904762 + 4.694444446

Combine like terms: 0.04761904762 + 4.694444446 = 4.74206349362
4.694444446 + -4.333333333x + x2 = 4.74206349362

Factor a perfect square on the left side:
(x + -2.166666667)(x + -2.166666667) = 4.74206349362

Calculate the square root of the right side: 2.177627951

Break this problem into two subproblems by setting 
(x + -2.166666667) equal to 2.177627951 and -2.177627951.

Subproblem 1
x + -2.166666667 = 2.177627951

Simplifying
x + -2.166666667 = 2.177627951

Reorder the terms:
-2.166666667 + x = 2.177627951

Solving
-2.166666667 + x = 2.177627951

Solving for variable 'x'.

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

Add '2.166666667' to each side of the equation.
-2.166666667 + 2.166666667 + x = 2.177627951 + 2.166666667

Combine like terms: -2.166666667 + 2.166666667 = 0.000000000
0.000000000 + x = 2.177627951 + 2.166666667
x = 2.177627951 + 2.166666667

Combine like terms: 2.177627951 + 2.166666667 = 4.344294618
x = 4.344294618

Simplifying
x = 4.344294618

Subproblem 2
x + -2.166666667 = -2.177627951

Simplifying
x + -2.166666667 = -2.177627951

Reorder the terms:
-2.166666667 + x = -2.177627951

Solving
-2.166666667 + x = -2.177627951

Solving for variable 'x'.

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

Add '2.166666667' to each side of the equation.
-2.166666667 + 2.166666667 + x = -2.177627951 + 2.166666667

Combine like terms: -2.166666667 + 2.166666667 = 0.000000000
0.000000000 + x = -2.177627951 + 2.166666667
x = -2.177627951 + 2.166666667

Combine like terms: -2.177627951 + 2.166666667 = -0.010961284
x = -0.010961284

Simplifying
x = -0.010961284

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.344294618, -0.010961284}