-12x=3-5x^2

Solution for -12x=3-5x^2 equation:

Simplifying
-12x = 3 + -5x2

Solving
-12x = 3 + -5x2

Solving for variable 'x'.

Reorder the terms:
-3 + -12x + 5x2 = 3 + -5x2 + -3 + 5x2

Reorder the terms:
-3 + -12x + 5x2 = 3 + -3 + -5x2 + 5x2

Combine like terms: 3 + -3 = 0
-3 + -12x + 5x2 = 0 + -5x2 + 5x2
-3 + -12x + 5x2 = -5x2 + 5x2

Combine like terms: -5x2 + 5x2 = 0
-3 + -12x + 5x2 = 0

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

Divide each side by '5'.
-0.6 + -2.4x + x2 = 0

Move the constant term to the right:

Add '0.6' to each side of the equation.
-0.6 + -2.4x + 0.6 + x2 = 0 + 0.6

Reorder the terms:
-0.6 + 0.6 + -2.4x + x2 = 0 + 0.6

Combine like terms: -0.6 + 0.6 = 0.0
0.0 + -2.4x + x2 = 0 + 0.6
-2.4x + x2 = 0 + 0.6

Combine like terms: 0 + 0.6 = 0.6
-2.4x + x2 = 0.6

The x term is -2.4x.  Take half its coefficient (-1.2).
Square it (1.44) and add it to both sides.

Add '1.44' to each side of the equation.
-2.4x + 1.44 + x2 = 0.6 + 1.44

Reorder the terms:
1.44 + -2.4x + x2 = 0.6 + 1.44

Combine like terms: 0.6 + 1.44 = 2.04
1.44 + -2.4x + x2 = 2.04

Factor a perfect square on the left side:
(x + -1.2)(x + -1.2) = 2.04

Calculate the square root of the right side: 1.428285686

Break this problem into two subproblems by setting 
(x + -1.2) equal to 1.428285686 and -1.428285686.

Subproblem 1
x + -1.2 = 1.428285686

Simplifying
x + -1.2 = 1.428285686

Reorder the terms:
-1.2 + x = 1.428285686

Solving
-1.2 + x = 1.428285686

Solving for variable 'x'.

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

Add '1.2' to each side of the equation.
-1.2 + 1.2 + x = 1.428285686 + 1.2

Combine like terms: -1.2 + 1.2 = 0.0
0.0 + x = 1.428285686 + 1.2
x = 1.428285686 + 1.2

Combine like terms: 1.428285686 + 1.2 = 2.628285686
x = 2.628285686

Simplifying
x = 2.628285686

Subproblem 2
x + -1.2 = -1.428285686

Simplifying
x + -1.2 = -1.428285686

Reorder the terms:
-1.2 + x = -1.428285686

Solving
-1.2 + x = -1.428285686

Solving for variable 'x'.

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

Add '1.2' to each side of the equation.
-1.2 + 1.2 + x = -1.428285686 + 1.2

Combine like terms: -1.2 + 1.2 = 0.0
0.0 + x = -1.428285686 + 1.2
x = -1.428285686 + 1.2

Combine like terms: -1.428285686 + 1.2 = -0.228285686
x = -0.228285686

Simplifying
x = -0.228285686

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.628285686, -0.228285686}