(2x-1)(x+2)=49

Solution for (2x-1)(x+2)=49 equation:

Simplifying
(2x + -1)(x + 2) = 49

Reorder the terms:
(-1 + 2x)(x + 2) = 49

Reorder the terms:
(-1 + 2x)(2 + x) = 49

Multiply (-1 + 2x) * (2 + x)
(-1(2 + x) + 2x * (2 + x)) = 49
((2 * -1 + x * -1) + 2x * (2 + x)) = 49
((-2 + -1x) + 2x * (2 + x)) = 49
(-2 + -1x + (2 * 2x + x * 2x)) = 49
(-2 + -1x + (4x + 2x2)) = 49

Combine like terms: -1x + 4x = 3x
(-2 + 3x + 2x2) = 49

Solving
-2 + 3x + 2x2 = 49

Solving for variable 'x'.

Reorder the terms:
-2 + -49 + 3x + 2x2 = 49 + -49

Combine like terms: -2 + -49 = -51
-51 + 3x + 2x2 = 49 + -49

Combine like terms: 49 + -49 = 0
-51 + 3x + 2x2 = 0

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

Divide each side by '2'.
-25.5 + 1.5x + x2 = 0

Move the constant term to the right:

Add '25.5' to each side of the equation.
-25.5 + 1.5x + 25.5 + x2 = 0 + 25.5

Reorder the terms:
-25.5 + 25.5 + 1.5x + x2 = 0 + 25.5

Combine like terms: -25.5 + 25.5 = 0.0
0.0 + 1.5x + x2 = 0 + 25.5
1.5x + x2 = 0 + 25.5

Combine like terms: 0 + 25.5 = 25.5
1.5x + x2 = 25.5

The x term is 1.5x.  Take half its coefficient (0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
1.5x + 0.5625 + x2 = 25.5 + 0.5625

Reorder the terms:
0.5625 + 1.5x + x2 = 25.5 + 0.5625

Combine like terms: 25.5 + 0.5625 = 26.0625
0.5625 + 1.5x + x2 = 26.0625

Factor a perfect square on the left side:
(x + 0.75)(x + 0.75) = 26.0625

Calculate the square root of the right side: 5.105144464

Break this problem into two subproblems by setting 
(x + 0.75) equal to 5.105144464 and -5.105144464.

Subproblem 1
x + 0.75 = 5.105144464

Simplifying
x + 0.75 = 5.105144464

Reorder the terms:
0.75 + x = 5.105144464

Solving
0.75 + x = 5.105144464

Solving for variable 'x'.

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

Add '-0.75' to each side of the equation.
0.75 + -0.75 + x = 5.105144464 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + x = 5.105144464 + -0.75
x = 5.105144464 + -0.75

Combine like terms: 5.105144464 + -0.75 = 4.355144464
x = 4.355144464

Simplifying
x = 4.355144464

Subproblem 2
x + 0.75 = -5.105144464

Simplifying
x + 0.75 = -5.105144464

Reorder the terms:
0.75 + x = -5.105144464

Solving
0.75 + x = -5.105144464

Solving for variable 'x'.

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

Add '-0.75' to each side of the equation.
0.75 + -0.75 + x = -5.105144464 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + x = -5.105144464 + -0.75
x = -5.105144464 + -0.75

Combine like terms: -5.105144464 + -0.75 = -5.855144464
x = -5.855144464

Simplifying
x = -5.855144464

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.355144464, -5.855144464}