(2x+1)(3x-2)=5(4x-1)

Solution for (2x+1)(3x-2)=5(4x-1) equation:

Simplifying
(2x + 1)(3x + -2) = 5(4x + -1)

Reorder the terms:
(1 + 2x)(3x + -2) = 5(4x + -1)

Reorder the terms:
(1 + 2x)(-2 + 3x) = 5(4x + -1)

Multiply (1 + 2x) * (-2 + 3x)
(1(-2 + 3x) + 2x * (-2 + 3x)) = 5(4x + -1)
((-2 * 1 + 3x * 1) + 2x * (-2 + 3x)) = 5(4x + -1)
((-2 + 3x) + 2x * (-2 + 3x)) = 5(4x + -1)
(-2 + 3x + (-2 * 2x + 3x * 2x)) = 5(4x + -1)
(-2 + 3x + (-4x + 6x2)) = 5(4x + -1)

Combine like terms: 3x + -4x = -1x
(-2 + -1x + 6x2) = 5(4x + -1)

Reorder the terms:
-2 + -1x + 6x2 = 5(-1 + 4x)
-2 + -1x + 6x2 = (-1 * 5 + 4x * 5)
-2 + -1x + 6x2 = (-5 + 20x)

Solving
-2 + -1x + 6x2 = -5 + 20x

Solving for variable 'x'.

Reorder the terms:
-2 + 5 + -1x + -20x + 6x2 = -5 + 20x + 5 + -20x

Combine like terms: -2 + 5 = 3
3 + -1x + -20x + 6x2 = -5 + 20x + 5 + -20x

Combine like terms: -1x + -20x = -21x
3 + -21x + 6x2 = -5 + 20x + 5 + -20x

Reorder the terms:
3 + -21x + 6x2 = -5 + 5 + 20x + -20x

Combine like terms: -5 + 5 = 0
3 + -21x + 6x2 = 0 + 20x + -20x
3 + -21x + 6x2 = 20x + -20x

Combine like terms: 20x + -20x = 0
3 + -21x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(1 + -7x + 2x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(1 + -7x + 2x2)' equal to zero and attempt to solve:

Simplifying
1 + -7x + 2x2 = 0

Solving
1 + -7x + 2x2 = 0

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

Divide each side by '2'.
0.5 + -3.5x + x2 = 0

Move the constant term to the right:

Add '-0.5' to each side of the equation.
0.5 + -3.5x + -0.5 + x2 = 0 + -0.5

Reorder the terms:
0.5 + -0.5 + -3.5x + x2 = 0 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + -3.5x + x2 = 0 + -0.5
-3.5x + x2 = 0 + -0.5

Combine like terms: 0 + -0.5 = -0.5
-3.5x + x2 = -0.5

The x term is -3.5x.  Take half its coefficient (-1.75).
Square it (3.0625) and add it to both sides.

Add '3.0625' to each side of the equation.
-3.5x + 3.0625 + x2 = -0.5 + 3.0625

Reorder the terms:
3.0625 + -3.5x + x2 = -0.5 + 3.0625

Combine like terms: -0.5 + 3.0625 = 2.5625
3.0625 + -3.5x + x2 = 2.5625

Factor a perfect square on the left side:
(x + -1.75)(x + -1.75) = 2.5625

Calculate the square root of the right side: 1.600781059

Break this problem into two subproblems by setting 
(x + -1.75) equal to 1.600781059 and -1.600781059.

Subproblem 1
x + -1.75 = 1.600781059

Simplifying
x + -1.75 = 1.600781059

Reorder the terms:
-1.75 + x = 1.600781059

Solving
-1.75 + x = 1.600781059

Solving for variable 'x'.

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

Add '1.75' to each side of the equation.
-1.75 + 1.75 + x = 1.600781059 + 1.75

Combine like terms: -1.75 + 1.75 = 0.00
0.00 + x = 1.600781059 + 1.75
x = 1.600781059 + 1.75

Combine like terms: 1.600781059 + 1.75 = 3.350781059
x = 3.350781059

Simplifying
x = 3.350781059

Subproblem 2
x + -1.75 = -1.600781059

Simplifying
x + -1.75 = -1.600781059

Reorder the terms:
-1.75 + x = -1.600781059

Solving
-1.75 + x = -1.600781059

Solving for variable 'x'.

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

Add '1.75' to each side of the equation.
-1.75 + 1.75 + x = -1.600781059 + 1.75

Combine like terms: -1.75 + 1.75 = 0.00
0.00 + x = -1.600781059 + 1.75
x = -1.600781059 + 1.75

Combine like terms: -1.600781059 + 1.75 = 0.149218941
x = 0.149218941

Simplifying
x = 0.149218941

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.350781059, 0.149218941}
Solution
x = {3.350781059, 0.149218941}