-7(x+2)3x+7=7x+8

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Solution for -7(x+2)3x+7=7x+8 equation: 


Simplifying
-7(x + 2) * 3x + 7 = 7x + 8

Reorder the terms:
-7(2 + x) * 3x + 7 = 7x + 8

Reorder the terms for easier multiplication:
-7 * 3x(2 + x) + 7 = 7x + 8

Multiply -7 * 3
-21x(2 + x) + 7 = 7x + 8
(2 * -21x + x * -21x) + 7 = 7x + 8
(-42x + -21x2) + 7 = 7x + 8

Reorder the terms:
7 + -42x + -21x2 = 7x + 8

Reorder the terms:
7 + -42x + -21x2 = 8 + 7x

Solving
7 + -42x + -21x2 = 8 + 7x

Solving for variable 'x'.

Reorder the terms:
7 + -8 + -42x + -7x + -21x2 = 8 + 7x + -8 + -7x

Combine like terms: 7 + -8 = -1
-1 + -42x + -7x + -21x2 = 8 + 7x + -8 + -7x

Combine like terms: -42x + -7x = -49x
-1 + -49x + -21x2 = 8 + 7x + -8 + -7x

Reorder the terms:
-1 + -49x + -21x2 = 8 + -8 + 7x + -7x

Combine like terms: 8 + -8 = 0
-1 + -49x + -21x2 = 0 + 7x + -7x
-1 + -49x + -21x2 = 7x + -7x

Combine like terms: 7x + -7x = 0
-1 + -49x + -21x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(1 + 49x + 21x2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(1 + 49x + 21x2)' equal to zero and attempt to solve:

Simplifying
1 + 49x + 21x2 = 0

Solving
1 + 49x + 21x2 = 0

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

Divide each side by '21'.
0.04761904762 + 2.333333333x + x2 = 0

Move the constant term to the right:

Add '-0.04761904762' to each side of the equation.
0.04761904762 + 2.333333333x + -0.04761904762 + x2 = 0 + -0.04761904762

Reorder the terms:
0.04761904762 + -0.04761904762 + 2.333333333x + x2 = 0 + -0.04761904762

Combine like terms: 0.04761904762 + -0.04761904762 = 0.00000000000
0.00000000000 + 2.333333333x + x2 = 0 + -0.04761904762
2.333333333x + x2 = 0 + -0.04761904762

Combine like terms: 0 + -0.04761904762 = -0.04761904762
2.333333333x + x2 = -0.04761904762

The x term is 2.333333333x.  Take half its coefficient (1.166666667).
Square it (1.361111112) and add it to both sides.

Add '1.361111112' to each side of the equation.
2.333333333x + 1.361111112 + x2 = -0.04761904762 + 1.361111112

Reorder the terms:
1.361111112 + 2.333333333x + x2 = -0.04761904762 + 1.361111112

Combine like terms: -0.04761904762 + 1.361111112 = 1.31349206438
1.361111112 + 2.333333333x + x2 = 1.31349206438

Factor a perfect square on the left side:
(x + 1.166666667)(x + 1.166666667) = 1.31349206438

Calculate the square root of the right side: 1.146076814

Break this problem into two subproblems by setting 
(x + 1.166666667) equal to 1.146076814 and -1.146076814.


Subproblem 1
x + 1.166666667 = 1.146076814

Simplifying
x + 1.166666667 = 1.146076814

Reorder the terms:
1.166666667 + x = 1.146076814

Solving
1.166666667 + x = 1.146076814

Solving for variable 'x'.

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

Add '-1.166666667' to each side of the equation.
1.166666667 + -1.166666667 + x = 1.146076814 + -1.166666667

Combine like terms: 1.166666667 + -1.166666667 = 0.000000000
0.000000000 + x = 1.146076814 + -1.166666667
x = 1.146076814 + -1.166666667

Combine like terms: 1.146076814 + -1.166666667 = -0.020589853
x = -0.020589853

Simplifying
x = -0.020589853


Subproblem 2
x + 1.166666667 = -1.146076814

Simplifying
x + 1.166666667 = -1.146076814

Reorder the terms:
1.166666667 + x = -1.146076814

Solving
1.166666667 + x = -1.146076814

Solving for variable 'x'.

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

Add '-1.166666667' to each side of the equation.
1.166666667 + -1.166666667 + x = -1.146076814 + -1.166666667

Combine like terms: 1.166666667 + -1.166666667 = 0.000000000
0.000000000 + x = -1.146076814 + -1.166666667
x = -1.146076814 + -1.166666667

Combine like terms: -1.146076814 + -1.166666667 = -2.312743481
x = -2.312743481

Simplifying
x = -2.312743481


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.020589853, -2.312743481}
Solution
x = {-0.020589853, -2.312743481}

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