4x(2x-7)=3x+(5x-7)(x+6)-25

Solution for 4x(2x-7)=3x+(5x-7)(x+6)-25 equation:

Simplifying
4x(2x + -7) = 3x + (5x + -7)(x + 6) + -25

Reorder the terms:
4x(-7 + 2x) = 3x + (5x + -7)(x + 6) + -25
(-7 * 4x + 2x * 4x) = 3x + (5x + -7)(x + 6) + -25
(-28x + 8x2) = 3x + (5x + -7)(x + 6) + -25

Reorder the terms:
-28x + 8x2 = 3x + (-7 + 5x)(x + 6) + -25

Reorder the terms:
-28x + 8x2 = 3x + (-7 + 5x)(6 + x) + -25

Multiply (-7 + 5x) * (6 + x)
-28x + 8x2 = 3x + (-7(6 + x) + 5x * (6 + x)) + -25
-28x + 8x2 = 3x + ((6 * -7 + x * -7) + 5x * (6 + x)) + -25
-28x + 8x2 = 3x + ((-42 + -7x) + 5x * (6 + x)) + -25
-28x + 8x2 = 3x + (-42 + -7x + (6 * 5x + x * 5x)) + -25
-28x + 8x2 = 3x + (-42 + -7x + (30x + 5x2)) + -25

Combine like terms: -7x + 30x = 23x
-28x + 8x2 = 3x + (-42 + 23x + 5x2) + -25

Reorder the terms:
-28x + 8x2 = -42 + -25 + 3x + 23x + 5x2

Combine like terms: -42 + -25 = -67
-28x + 8x2 = -67 + 3x + 23x + 5x2

Combine like terms: 3x + 23x = 26x
-28x + 8x2 = -67 + 26x + 5x2

Solving
-28x + 8x2 = -67 + 26x + 5x2

Solving for variable 'x'.

Reorder the terms:
67 + -28x + -26x + 8x2 + -5x2 = -67 + 26x + 5x2 + 67 + -26x + -5x2

Combine like terms: -28x + -26x = -54x
67 + -54x + 8x2 + -5x2 = -67 + 26x + 5x2 + 67 + -26x + -5x2

Combine like terms: 8x2 + -5x2 = 3x2
67 + -54x + 3x2 = -67 + 26x + 5x2 + 67 + -26x + -5x2

Reorder the terms:
67 + -54x + 3x2 = -67 + 67 + 26x + -26x + 5x2 + -5x2

Combine like terms: -67 + 67 = 0
67 + -54x + 3x2 = 0 + 26x + -26x + 5x2 + -5x2
67 + -54x + 3x2 = 26x + -26x + 5x2 + -5x2

Combine like terms: 26x + -26x = 0
67 + -54x + 3x2 = 0 + 5x2 + -5x2
67 + -54x + 3x2 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
67 + -54x + 3x2 = 0

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

Divide each side by '3'.
22.33333333 + -18x + x2 = 0

Move the constant term to the right:

Add '-22.33333333' to each side of the equation.
22.33333333 + -18x + -22.33333333 + x2 = 0 + -22.33333333

Reorder the terms:
22.33333333 + -22.33333333 + -18x + x2 = 0 + -22.33333333

Combine like terms: 22.33333333 + -22.33333333 = 0.00000000
0.00000000 + -18x + x2 = 0 + -22.33333333
-18x + x2 = 0 + -22.33333333

Combine like terms: 0 + -22.33333333 = -22.33333333
-18x + x2 = -22.33333333

The x term is -18x.  Take half its coefficient (-9).
Square it (81) and add it to both sides.

Add '81' to each side of the equation.
-18x + 81 + x2 = -22.33333333 + 81

Reorder the terms:
81 + -18x + x2 = -22.33333333 + 81

Combine like terms: -22.33333333 + 81 = 58.66666667
81 + -18x + x2 = 58.66666667

Factor a perfect square on the left side:
(x + -9)(x + -9) = 58.66666667

Calculate the square root of the right side: 7.659416862

Break this problem into two subproblems by setting 
(x + -9) equal to 7.659416862 and -7.659416862.

Subproblem 1
x + -9 = 7.659416862

Simplifying
x + -9 = 7.659416862

Reorder the terms:
-9 + x = 7.659416862

Solving
-9 + x = 7.659416862

Solving for variable 'x'.

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

Add '9' to each side of the equation.
-9 + 9 + x = 7.659416862 + 9

Combine like terms: -9 + 9 = 0
0 + x = 7.659416862 + 9
x = 7.659416862 + 9

Combine like terms: 7.659416862 + 9 = 16.659416862
x = 16.659416862

Simplifying
x = 16.659416862

Subproblem 2
x + -9 = -7.659416862

Simplifying
x + -9 = -7.659416862

Reorder the terms:
-9 + x = -7.659416862

Solving
-9 + x = -7.659416862

Solving for variable 'x'.

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

Add '9' to each side of the equation.
-9 + 9 + x = -7.659416862 + 9

Combine like terms: -9 + 9 = 0
0 + x = -7.659416862 + 9
x = -7.659416862 + 9

Combine like terms: -7.659416862 + 9 = 1.340583138
x = 1.340583138

Simplifying
x = 1.340583138

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {16.659416862, 1.340583138}