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

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

Simplifying
5(5x + -4) + x(4x + 3) = 0

Reorder the terms:
5(-4 + 5x) + x(4x + 3) = 0
(-4 * 5 + 5x * 5) + x(4x + 3) = 0
(-20 + 25x) + x(4x + 3) = 0

Reorder the terms:
-20 + 25x + x(3 + 4x) = 0
-20 + 25x + (3 * x + 4x * x) = 0
-20 + 25x + (3x + 4x2) = 0

Combine like terms: 25x + 3x = 28x
-20 + 28x + 4x2 = 0

Solving
-20 + 28x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-5 + 7x + x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-5 + 7x + x2)' equal to zero and attempt to solve:

Simplifying
-5 + 7x + x2 = 0

Solving
-5 + 7x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + 7x + 5 + x2 = 0 + 5

Reorder the terms:
-5 + 5 + 7x + x2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + 7x + x2 = 0 + 5
7x + x2 = 0 + 5

Combine like terms: 0 + 5 = 5
7x + x2 = 5

The x term is 7x.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7x + 12.25 + x2 = 5 + 12.25

Reorder the terms:
12.25 + 7x + x2 = 5 + 12.25

Combine like terms: 5 + 12.25 = 17.25
12.25 + 7x + x2 = 17.25

Factor a perfect square on the left side:
(x + 3.5)(x + 3.5) = 17.25

Calculate the square root of the right side: 4.153311931

Break this problem into two subproblems by setting 
(x + 3.5) equal to 4.153311931 and -4.153311931.

Subproblem 1
x + 3.5 = 4.153311931

Simplifying
x + 3.5 = 4.153311931

Reorder the terms:
3.5 + x = 4.153311931

Solving
3.5 + x = 4.153311931

Solving for variable 'x'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + x = 4.153311931 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = 4.153311931 + -3.5
x = 4.153311931 + -3.5

Combine like terms: 4.153311931 + -3.5 = 0.653311931
x = 0.653311931

Simplifying
x = 0.653311931

Subproblem 2
x + 3.5 = -4.153311931

Simplifying
x + 3.5 = -4.153311931

Reorder the terms:
3.5 + x = -4.153311931

Solving
3.5 + x = -4.153311931

Solving for variable 'x'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + x = -4.153311931 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = -4.153311931 + -3.5
x = -4.153311931 + -3.5

Combine like terms: -4.153311931 + -3.5 = -7.653311931
x = -7.653311931

Simplifying
x = -7.653311931

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.653311931, -7.653311931}
Solution
x = {0.653311931, -7.653311931}