7(x+2)5x+21=

Solution for 7(x+2)5x+21= equation:

Simplifying
7(x + 2) * 5x + 21 = 0

Reorder the terms:
7(2 + x) * 5x + 21 = 0

Reorder the terms for easier multiplication:
7 * 5x(2 + x) + 21 = 0

Multiply 7 * 5
35x(2 + x) + 21 = 0
(2 * 35x + x * 35x) + 21 = 0
(70x + 35x2) + 21 = 0

Reorder the terms:
21 + 70x + 35x2 = 0

Solving
21 + 70x + 35x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '7'.
7(3 + 10x + 5x2) = 0

Ignore the factor 7.
Subproblem 1
Set the factor '(3 + 10x + 5x2)' equal to zero and attempt to solve:

Simplifying
3 + 10x + 5x2 = 0

Solving
3 + 10x + 5x2 = 0

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

Divide each side by '5'.
0.6 + 2x + x2 = 0

Move the constant term to the right:

Add '-0.6' to each side of the equation.
0.6 + 2x + -0.6 + x2 = 0 + -0.6

Reorder the terms:
0.6 + -0.6 + 2x + x2 = 0 + -0.6

Combine like terms: 0.6 + -0.6 = 0.0
0.0 + 2x + x2 = 0 + -0.6
2x + x2 = 0 + -0.6

Combine like terms: 0 + -0.6 = -0.6
2x + x2 = -0.6

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 = -0.6 + 1

Reorder the terms:
1 + 2x + x2 = -0.6 + 1

Combine like terms: -0.6 + 1 = 0.4
1 + 2x + x2 = 0.4

Factor a perfect square on the left side:
(x + 1)(x + 1) = 0.4

Calculate the square root of the right side: 0.632455532

Break this problem into two subproblems by setting 
(x + 1) equal to 0.632455532 and -0.632455532.

Subproblem 1
x + 1 = 0.632455532

Simplifying
x + 1 = 0.632455532

Reorder the terms:
1 + x = 0.632455532

Solving
1 + x = 0.632455532

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 = 0.632455532 + -1

Combine like terms: 1 + -1 = 0
0 + x = 0.632455532 + -1
x = 0.632455532 + -1

Combine like terms: 0.632455532 + -1 = -0.367544468
x = -0.367544468

Simplifying
x = -0.367544468

Subproblem 2
x + 1 = -0.632455532

Simplifying
x + 1 = -0.632455532

Reorder the terms:
1 + x = -0.632455532

Solving
1 + x = -0.632455532

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 = -0.632455532 + -1

Combine like terms: 1 + -1 = 0
0 + x = -0.632455532 + -1
x = -0.632455532 + -1

Combine like terms: -0.632455532 + -1 = -1.632455532
x = -1.632455532

Simplifying
x = -1.632455532

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.367544468, -1.632455532}
Solution
x = {-0.367544468, -1.632455532}