62+4(x+2)5x-7=180

Solution for 62+4(x+2)5x-7=180 equation:

Simplifying
62 + 4(x + 2) * 5x + -7 = 180

Reorder the terms:
62 + 4(2 + x) * 5x + -7 = 180

Reorder the terms for easier multiplication:
62 + 4 * 5x(2 + x) + -7 = 180

Multiply 4 * 5
62 + 20x(2 + x) + -7 = 180
62 + (2 * 20x + x * 20x) + -7 = 180
62 + (40x + 20x2) + -7 = 180

Reorder the terms:
62 + -7 + 40x + 20x2 = 180

Combine like terms: 62 + -7 = 55
55 + 40x + 20x2 = 180

Solving
55 + 40x + 20x2 = 180

Solving for variable 'x'.

Reorder the terms:
55 + -180 + 40x + 20x2 = 180 + -180

Combine like terms: 55 + -180 = -125
-125 + 40x + 20x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-125 + 40x + 20x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-25 + 8x + 4x2) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(-25 + 8x + 4x2)' equal to zero and attempt to solve:

Simplifying
-25 + 8x + 4x2 = 0

Solving
-25 + 8x + 4x2 = 0

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

Divide each side by '4'.
-6.25 + 2x + x2 = 0

Move the constant term to the right:

Add '6.25' to each side of the equation.
-6.25 + 2x + 6.25 + x2 = 0 + 6.25

Reorder the terms:
-6.25 + 6.25 + 2x + x2 = 0 + 6.25

Combine like terms: -6.25 + 6.25 = 0.00
0.00 + 2x + x2 = 0 + 6.25
2x + x2 = 0 + 6.25

Combine like terms: 0 + 6.25 = 6.25
2x + x2 = 6.25

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 = 6.25 + 1

Reorder the terms:
1 + 2x + x2 = 6.25 + 1

Combine like terms: 6.25 + 1 = 7.25
1 + 2x + x2 = 7.25

Factor a perfect square on the left side:
(x + 1)(x + 1) = 7.25

Calculate the square root of the right side: 2.692582404

Break this problem into two subproblems by setting 
(x + 1) equal to 2.692582404 and -2.692582404.

Subproblem 1
x + 1 = 2.692582404

Simplifying
x + 1 = 2.692582404

Reorder the terms:
1 + x = 2.692582404

Solving
1 + x = 2.692582404

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 = 2.692582404 + -1

Combine like terms: 1 + -1 = 0
0 + x = 2.692582404 + -1
x = 2.692582404 + -1

Combine like terms: 2.692582404 + -1 = 1.692582404
x = 1.692582404

Simplifying
x = 1.692582404

Subproblem 2
x + 1 = -2.692582404

Simplifying
x + 1 = -2.692582404

Reorder the terms:
1 + x = -2.692582404

Solving
1 + x = -2.692582404

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 = -2.692582404 + -1

Combine like terms: 1 + -1 = 0
0 + x = -2.692582404 + -1
x = -2.692582404 + -1

Combine like terms: -2.692582404 + -1 = -3.692582404
x = -3.692582404

Simplifying
x = -3.692582404

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.692582404, -3.692582404}
Solution
x = {1.692582404, -3.692582404}