4(5+2x)0-5=3*x(3x+7)

Solution for 4(5+2x)0-5=3*x(3x+7) equation:

Simplifying
4(5 + 2x) * 0 + -5 = 3x(3x + 7)

Reorder the terms for easier multiplication:
4 * 0(5 + 2x) + -5 = 3x(3x + 7)

Multiply 4 * 0
0(5 + 2x) + -5 = 3x(3x + 7)

Anything times zero is zero.
0(5 + 2x) + -5 = 3x(3x + 7)

Combine like terms: 0 + -5 = -5
-5 = 3x(3x + 7)

Reorder the terms:
-5 = 3x(7 + 3x)
-5 = (7 * 3x + 3x * 3x)
-5 = (21x + 9x2)

Solving
-5 = 21x + 9x2

Solving for variable 'x'.

Reorder the terms:
-5 + -21x + -9x2 = 21x + -21x + 9x2 + -9x2

Combine like terms: 21x + -21x = 0
-5 + -21x + -9x2 = 0 + 9x2 + -9x2
-5 + -21x + -9x2 = 9x2 + -9x2

Combine like terms: 9x2 + -9x2 = 0
-5 + -21x + -9x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(5 + 21x + 9x2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(5 + 21x + 9x2)' equal to zero and attempt to solve:

Simplifying
5 + 21x + 9x2 = 0

Solving
5 + 21x + 9x2 = 0

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

Divide each side by '9'.
0.5555555556 + 2.333333333x + x2 = 0

Move the constant term to the right:

Add '-0.5555555556' to each side of the equation.
0.5555555556 + 2.333333333x + -0.5555555556 + x2 = 0 + -0.5555555556

Reorder the terms:
0.5555555556 + -0.5555555556 + 2.333333333x + x2 = 0 + -0.5555555556

Combine like terms: 0.5555555556 + -0.5555555556 = 0.0000000000
0.0000000000 + 2.333333333x + x2 = 0 + -0.5555555556
2.333333333x + x2 = 0 + -0.5555555556

Combine like terms: 0 + -0.5555555556 = -0.5555555556
2.333333333x + x2 = -0.5555555556

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 = -0.5555555556 + 1.361111112

Reorder the terms:
1.361111112 + 2.333333333x + x2 = -0.5555555556 + 1.361111112

Combine like terms: -0.5555555556 + 1.361111112 = 0.8055555564
1.361111112 + 2.333333333x + x2 = 0.8055555564

Factor a perfect square on the left side:
(x + 1.166666667)(x + 1.166666667) = 0.8055555564

Calculate the square root of the right side: 0.897527468

Break this problem into two subproblems by setting 
(x + 1.166666667) equal to 0.897527468 and -0.897527468.

Subproblem 1
x + 1.166666667 = 0.897527468

Simplifying
x + 1.166666667 = 0.897527468

Reorder the terms:
1.166666667 + x = 0.897527468

Solving
1.166666667 + x = 0.897527468

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 = 0.897527468 + -1.166666667

Combine like terms: 1.166666667 + -1.166666667 = 0.000000000
0.000000000 + x = 0.897527468 + -1.166666667
x = 0.897527468 + -1.166666667

Combine like terms: 0.897527468 + -1.166666667 = -0.269139199
x = -0.269139199

Simplifying
x = -0.269139199

Subproblem 2
x + 1.166666667 = -0.897527468

Simplifying
x + 1.166666667 = -0.897527468

Reorder the terms:
1.166666667 + x = -0.897527468

Solving
1.166666667 + x = -0.897527468

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 = -0.897527468 + -1.166666667

Combine like terms: 1.166666667 + -1.166666667 = 0.000000000
0.000000000 + x = -0.897527468 + -1.166666667
x = -0.897527468 + -1.166666667

Combine like terms: -0.897527468 + -1.166666667 = -2.064194135
x = -2.064194135

Simplifying
x = -2.064194135

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.269139199, -2.064194135}
Solution
x = {-0.269139199, -2.064194135}