4x^2-19+21=-3x+6

Solution for 4x^2-19+21=-3x+6 equation:

Simplifying
4x2 + -19 + 21 = -3x + 6

Reorder the terms:
-19 + 21 + 4x2 = -3x + 6

Combine like terms: -19 + 21 = 2
2 + 4x2 = -3x + 6

Reorder the terms:
2 + 4x2 = 6 + -3x

Solving
2 + 4x2 = 6 + -3x

Solving for variable 'x'.

Reorder the terms:
2 + -6 + 3x + 4x2 = 6 + -3x + -6 + 3x

Combine like terms: 2 + -6 = -4
-4 + 3x + 4x2 = 6 + -3x + -6 + 3x

Reorder the terms:
-4 + 3x + 4x2 = 6 + -6 + -3x + 3x

Combine like terms: 6 + -6 = 0
-4 + 3x + 4x2 = 0 + -3x + 3x
-4 + 3x + 4x2 = -3x + 3x

Combine like terms: -3x + 3x = 0
-4 + 3x + 4x2 = 0

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

Divide each side by '4'.
-1 + 0.75x + x2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 0.75x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + 0.75x + x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 0.75x + x2 = 0 + 1
0.75x + x2 = 0 + 1

Combine like terms: 0 + 1 = 1
0.75x + x2 = 1

The x term is 0.75x.  Take half its coefficient (0.375).
Square it (0.140625) and add it to both sides.

Add '0.140625' to each side of the equation.
0.75x + 0.140625 + x2 = 1 + 0.140625

Reorder the terms:
0.140625 + 0.75x + x2 = 1 + 0.140625

Combine like terms: 1 + 0.140625 = 1.140625
0.140625 + 0.75x + x2 = 1.140625

Factor a perfect square on the left side:
(x + 0.375)(x + 0.375) = 1.140625

Calculate the square root of the right side: 1.068000468

Break this problem into two subproblems by setting 
(x + 0.375) equal to 1.068000468 and -1.068000468.

Subproblem 1
x + 0.375 = 1.068000468

Simplifying
x + 0.375 = 1.068000468

Reorder the terms:
0.375 + x = 1.068000468

Solving
0.375 + x = 1.068000468

Solving for variable 'x'.

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

Add '-0.375' to each side of the equation.
0.375 + -0.375 + x = 1.068000468 + -0.375

Combine like terms: 0.375 + -0.375 = 0.000
0.000 + x = 1.068000468 + -0.375
x = 1.068000468 + -0.375

Combine like terms: 1.068000468 + -0.375 = 0.693000468
x = 0.693000468

Simplifying
x = 0.693000468

Subproblem 2
x + 0.375 = -1.068000468

Simplifying
x + 0.375 = -1.068000468

Reorder the terms:
0.375 + x = -1.068000468

Solving
0.375 + x = -1.068000468

Solving for variable 'x'.

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

Add '-0.375' to each side of the equation.
0.375 + -0.375 + x = -1.068000468 + -0.375

Combine like terms: 0.375 + -0.375 = 0.000
0.000 + x = -1.068000468 + -0.375
x = -1.068000468 + -0.375

Combine like terms: -1.068000468 + -0.375 = -1.443000468
x = -1.443000468

Simplifying
x = -1.443000468

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.693000468, -1.443000468}