9x^2-4x+4=-12x+3

Solution for 9x^2-4x+4=-12x+3 equation:

Simplifying
9x2 + -4x + 4 = -12x + 3

Reorder the terms:
4 + -4x + 9x2 = -12x + 3

Reorder the terms:
4 + -4x + 9x2 = 3 + -12x

Solving
4 + -4x + 9x2 = 3 + -12x

Solving for variable 'x'.

Reorder the terms:
4 + -3 + -4x + 12x + 9x2 = 3 + -12x + -3 + 12x

Combine like terms: 4 + -3 = 1
1 + -4x + 12x + 9x2 = 3 + -12x + -3 + 12x

Combine like terms: -4x + 12x = 8x
1 + 8x + 9x2 = 3 + -12x + -3 + 12x

Reorder the terms:
1 + 8x + 9x2 = 3 + -3 + -12x + 12x

Combine like terms: 3 + -3 = 0
1 + 8x + 9x2 = 0 + -12x + 12x
1 + 8x + 9x2 = -12x + 12x

Combine like terms: -12x + 12x = 0
1 + 8x + 9x2 = 0

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

Divide each side by '9'.
0.1111111111 + 0.8888888889x + x2 = 0

Move the constant term to the right:

Add '-0.1111111111' to each side of the equation.
0.1111111111 + 0.8888888889x + -0.1111111111 + x2 = 0 + -0.1111111111

Reorder the terms:
0.1111111111 + -0.1111111111 + 0.8888888889x + x2 = 0 + -0.1111111111

Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000
0.0000000000 + 0.8888888889x + x2 = 0 + -0.1111111111
0.8888888889x + x2 = 0 + -0.1111111111

Combine like terms: 0 + -0.1111111111 = -0.1111111111
0.8888888889x + x2 = -0.1111111111

The x term is 0.8888888889x.  Take half its coefficient (0.4444444445).
Square it (0.1975308642) and add it to both sides.

Add '0.1975308642' to each side of the equation.
0.8888888889x + 0.1975308642 + x2 = -0.1111111111 + 0.1975308642

Reorder the terms:
0.1975308642 + 0.8888888889x + x2 = -0.1111111111 + 0.1975308642

Combine like terms: -0.1111111111 + 0.1975308642 = 0.0864197531
0.1975308642 + 0.8888888889x + x2 = 0.0864197531

Factor a perfect square on the left side:
(x + 0.4444444445)(x + 0.4444444445) = 0.0864197531

Calculate the square root of the right side: 0.293972368

Break this problem into two subproblems by setting 
(x + 0.4444444445) equal to 0.293972368 and -0.293972368.

Subproblem 1
x + 0.4444444445 = 0.293972368

Simplifying
x + 0.4444444445 = 0.293972368

Reorder the terms:
0.4444444445 + x = 0.293972368

Solving
0.4444444445 + x = 0.293972368

Solving for variable 'x'.

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

Add '-0.4444444445' to each side of the equation.
0.4444444445 + -0.4444444445 + x = 0.293972368 + -0.4444444445

Combine like terms: 0.4444444445 + -0.4444444445 = 0.0000000000
0.0000000000 + x = 0.293972368 + -0.4444444445
x = 0.293972368 + -0.4444444445

Combine like terms: 0.293972368 + -0.4444444445 = -0.1504720765
x = -0.1504720765

Simplifying
x = -0.1504720765

Subproblem 2
x + 0.4444444445 = -0.293972368

Simplifying
x + 0.4444444445 = -0.293972368

Reorder the terms:
0.4444444445 + x = -0.293972368

Solving
0.4444444445 + x = -0.293972368

Solving for variable 'x'.

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

Add '-0.4444444445' to each side of the equation.
0.4444444445 + -0.4444444445 + x = -0.293972368 + -0.4444444445

Combine like terms: 0.4444444445 + -0.4444444445 = 0.0000000000
0.0000000000 + x = -0.293972368 + -0.4444444445
x = -0.293972368 + -0.4444444445

Combine like terms: -0.293972368 + -0.4444444445 = -0.7384168125
x = -0.7384168125

Simplifying
x = -0.7384168125

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.1504720765, -0.7384168125}