4x(2x-5)-3(2x-5)=29

Solution for 4x(2x-5)-3(2x-5)=29 equation:

Simplifying
4x(2x + -5) + -3(2x + -5) = 29

Reorder the terms:
4x(-5 + 2x) + -3(2x + -5) = 29
(-5 * 4x + 2x * 4x) + -3(2x + -5) = 29
(-20x + 8x2) + -3(2x + -5) = 29

Reorder the terms:
-20x + 8x2 + -3(-5 + 2x) = 29
-20x + 8x2 + (-5 * -3 + 2x * -3) = 29
-20x + 8x2 + (15 + -6x) = 29

Reorder the terms:
15 + -20x + -6x + 8x2 = 29

Combine like terms: -20x + -6x = -26x
15 + -26x + 8x2 = 29

Solving
15 + -26x + 8x2 = 29

Solving for variable 'x'.

Reorder the terms:
15 + -29 + -26x + 8x2 = 29 + -29

Combine like terms: 15 + -29 = -14
-14 + -26x + 8x2 = 29 + -29

Combine like terms: 29 + -29 = 0
-14 + -26x + 8x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-7 + -13x + 4x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-7 + -13x + 4x2)' equal to zero and attempt to solve:

Simplifying
-7 + -13x + 4x2 = 0

Solving
-7 + -13x + 4x2 = 0

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

Divide each side by '4'.
-1.75 + -3.25x + x2 = 0

Move the constant term to the right:

Add '1.75' to each side of the equation.
-1.75 + -3.25x + 1.75 + x2 = 0 + 1.75

Reorder the terms:
-1.75 + 1.75 + -3.25x + x2 = 0 + 1.75

Combine like terms: -1.75 + 1.75 = 0.00
0.00 + -3.25x + x2 = 0 + 1.75
-3.25x + x2 = 0 + 1.75

Combine like terms: 0 + 1.75 = 1.75
-3.25x + x2 = 1.75

The x term is -3.25x.  Take half its coefficient (-1.625).
Square it (2.640625) and add it to both sides.

Add '2.640625' to each side of the equation.
-3.25x + 2.640625 + x2 = 1.75 + 2.640625

Reorder the terms:
2.640625 + -3.25x + x2 = 1.75 + 2.640625

Combine like terms: 1.75 + 2.640625 = 4.390625
2.640625 + -3.25x + x2 = 4.390625

Factor a perfect square on the left side:
(x + -1.625)(x + -1.625) = 4.390625

Calculate the square root of the right side: 2.095381827

Break this problem into two subproblems by setting 
(x + -1.625) equal to 2.095381827 and -2.095381827.

Subproblem 1
x + -1.625 = 2.095381827

Simplifying
x + -1.625 = 2.095381827

Reorder the terms:
-1.625 + x = 2.095381827

Solving
-1.625 + x = 2.095381827

Solving for variable 'x'.

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

Add '1.625' to each side of the equation.
-1.625 + 1.625 + x = 2.095381827 + 1.625

Combine like terms: -1.625 + 1.625 = 0.000
0.000 + x = 2.095381827 + 1.625
x = 2.095381827 + 1.625

Combine like terms: 2.095381827 + 1.625 = 3.720381827
x = 3.720381827

Simplifying
x = 3.720381827

Subproblem 2
x + -1.625 = -2.095381827

Simplifying
x + -1.625 = -2.095381827

Reorder the terms:
-1.625 + x = -2.095381827

Solving
-1.625 + x = -2.095381827

Solving for variable 'x'.

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

Add '1.625' to each side of the equation.
-1.625 + 1.625 + x = -2.095381827 + 1.625

Combine like terms: -1.625 + 1.625 = 0.000
0.000 + x = -2.095381827 + 1.625
x = -2.095381827 + 1.625

Combine like terms: -2.095381827 + 1.625 = -0.470381827
x = -0.470381827

Simplifying
x = -0.470381827

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.720381827, -0.470381827}
Solution
x = {3.720381827, -0.470381827}