(5x+4)(5x+6)=34

Solution for (5x+4)(5x+6)=34 equation:

Simplifying
(5x + 4)(5x + 6) = 34

Reorder the terms:
(4 + 5x)(5x + 6) = 34

Reorder the terms:
(4 + 5x)(6 + 5x) = 34

Multiply (4 + 5x) * (6 + 5x)
(4(6 + 5x) + 5x * (6 + 5x)) = 34
((6 * 4 + 5x * 4) + 5x * (6 + 5x)) = 34
((24 + 20x) + 5x * (6 + 5x)) = 34
(24 + 20x + (6 * 5x + 5x * 5x)) = 34
(24 + 20x + (30x + 25x2)) = 34

Combine like terms: 20x + 30x = 50x
(24 + 50x + 25x2) = 34

Solving
24 + 50x + 25x2 = 34

Solving for variable 'x'.

Reorder the terms:
24 + -34 + 50x + 25x2 = 34 + -34

Combine like terms: 24 + -34 = -10
-10 + 50x + 25x2 = 34 + -34

Combine like terms: 34 + -34 = 0
-10 + 50x + 25x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-2 + 10x + 5x2) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(-2 + 10x + 5x2)' equal to zero and attempt to solve:

Simplifying
-2 + 10x + 5x2 = 0

Solving
-2 + 10x + 5x2 = 0

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

Divide each side by '5'.
-0.4 + 2x + x2 = 0

Move the constant term to the right:

Add '0.4' to each side of the equation.
-0.4 + 2x + 0.4 + x2 = 0 + 0.4

Reorder the terms:
-0.4 + 0.4 + 2x + x2 = 0 + 0.4

Combine like terms: -0.4 + 0.4 = 0.0
0.0 + 2x + x2 = 0 + 0.4
2x + x2 = 0 + 0.4

Combine like terms: 0 + 0.4 = 0.4
2x + x2 = 0.4

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = 0.4 + 1

Reorder the terms:
1 + 2x + x2 = 0.4 + 1

Combine like terms: 0.4 + 1 = 1.4
1 + 2x + x2 = 1.4

Factor a perfect square on the left side:
(x + 1)(x + 1) = 1.4

Calculate the square root of the right side: 1.183215957

Break this problem into two subproblems by setting 
(x + 1) equal to 1.183215957 and -1.183215957.

Subproblem 1
x + 1 = 1.183215957

Simplifying
x + 1 = 1.183215957

Reorder the terms:
1 + x = 1.183215957

Solving
1 + x = 1.183215957

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = 1.183215957 + -1

Combine like terms: 1 + -1 = 0
0 + x = 1.183215957 + -1
x = 1.183215957 + -1

Combine like terms: 1.183215957 + -1 = 0.183215957
x = 0.183215957

Simplifying
x = 0.183215957

Subproblem 2
x + 1 = -1.183215957

Simplifying
x + 1 = -1.183215957

Reorder the terms:
1 + x = -1.183215957

Solving
1 + x = -1.183215957

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = -1.183215957 + -1

Combine like terms: 1 + -1 = 0
0 + x = -1.183215957 + -1
x = -1.183215957 + -1

Combine like terms: -1.183215957 + -1 = -2.183215957
x = -2.183215957

Simplifying
x = -2.183215957

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.183215957, -2.183215957}
Solution
x = {0.183215957, -2.183215957}