3x^2=4(3x)+3

Solution for 3x^2=4(3x)+3 equation:

Simplifying
3x2 = 4(3x) + 3

Remove parenthesis around (3x)
3x2 = 4 * 3x + 3

Multiply 4 * 3
3x2 = 12x + 3

Reorder the terms:
3x2 = 3 + 12x

Solving
3x2 = 3 + 12x

Solving for variable 'x'.

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

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

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

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

Factor out the Greatest Common Factor (GCF), '3'.
3(-1 + -4x + x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-1 + -4x + x2)' equal to zero and attempt to solve:

Simplifying
-1 + -4x + x2 = 0

Solving
-1 + -4x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -4x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + -4x + x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -4x + x2 = 0 + 1
-4x + x2 = 0 + 1

Combine like terms: 0 + 1 = 1
-4x + x2 = 1

The x term is -4x.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4x + 4 + x2 = 1 + 4

Reorder the terms:
4 + -4x + x2 = 1 + 4

Combine like terms: 1 + 4 = 5
4 + -4x + x2 = 5

Factor a perfect square on the left side:
(x + -2)(x + -2) = 5

Calculate the square root of the right side: 2.236067978

Break this problem into two subproblems by setting 
(x + -2) equal to 2.236067978 and -2.236067978.

Subproblem 1
x + -2 = 2.236067978

Simplifying
x + -2 = 2.236067978

Reorder the terms:
-2 + x = 2.236067978

Solving
-2 + x = 2.236067978

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = 2.236067978 + 2

Combine like terms: -2 + 2 = 0
0 + x = 2.236067978 + 2
x = 2.236067978 + 2

Combine like terms: 2.236067978 + 2 = 4.236067978
x = 4.236067978

Simplifying
x = 4.236067978

Subproblem 2
x + -2 = -2.236067978

Simplifying
x + -2 = -2.236067978

Reorder the terms:
-2 + x = -2.236067978

Solving
-2 + x = -2.236067978

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = -2.236067978 + 2

Combine like terms: -2 + 2 = 0
0 + x = -2.236067978 + 2
x = -2.236067978 + 2

Combine like terms: -2.236067978 + 2 = -0.236067978
x = -0.236067978

Simplifying
x = -0.236067978

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.236067978, -0.236067978}
Solution
x = {4.236067978, -0.236067978}