4x(5+5x)=3(3x+7)

Solution for 4x(5+5x)=3(3x+7) equation:

Simplifying
4x(5 + 5x) = 3(3x + 7)
(5 * 4x + 5x * 4x) = 3(3x + 7)
(20x + 20x2) = 3(3x + 7)

Reorder the terms:
20x + 20x2 = 3(7 + 3x)
20x + 20x2 = (7 * 3 + 3x * 3)
20x + 20x2 = (21 + 9x)

Solving
20x + 20x2 = 21 + 9x

Solving for variable 'x'.

Reorder the terms:
-21 + 20x + -9x + 20x2 = 21 + 9x + -21 + -9x

Combine like terms: 20x + -9x = 11x
-21 + 11x + 20x2 = 21 + 9x + -21 + -9x

Reorder the terms:
-21 + 11x + 20x2 = 21 + -21 + 9x + -9x

Combine like terms: 21 + -21 = 0
-21 + 11x + 20x2 = 0 + 9x + -9x
-21 + 11x + 20x2 = 9x + -9x

Combine like terms: 9x + -9x = 0
-21 + 11x + 20x2 = 0

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

Divide each side by '20'.
-1.05 + 0.55x + x2 = 0.0

Move the constant term to the right:

Add '1.05' to each side of the equation.
-1.05 + 0.55x + 1.05 + x2 = 0.0 + 1.05

Reorder the terms:
-1.05 + 1.05 + 0.55x + x2 = 0.0 + 1.05

Combine like terms: -1.05 + 1.05 = 0.00
0.00 + 0.55x + x2 = 0.0 + 1.05
0.55x + x2 = 0.0 + 1.05

Combine like terms: 0.0 + 1.05 = 1.05
0.55x + x2 = 1.05

The x term is 0.55x.  Take half its coefficient (0.275).
Square it (0.075625) and add it to both sides.

Add '0.075625' to each side of the equation.
0.55x + 0.075625 + x2 = 1.05 + 0.075625

Reorder the terms:
0.075625 + 0.55x + x2 = 1.05 + 0.075625

Combine like terms: 1.05 + 0.075625 = 1.125625
0.075625 + 0.55x + x2 = 1.125625

Factor a perfect square on the left side:
(x + 0.275)(x + 0.275) = 1.125625

Calculate the square root of the right side: 1.060954759

Break this problem into two subproblems by setting 
(x + 0.275) equal to 1.060954759 and -1.060954759.

Subproblem 1
x + 0.275 = 1.060954759

Simplifying
x + 0.275 = 1.060954759

Reorder the terms:
0.275 + x = 1.060954759

Solving
0.275 + x = 1.060954759

Solving for variable 'x'.

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

Add '-0.275' to each side of the equation.
0.275 + -0.275 + x = 1.060954759 + -0.275

Combine like terms: 0.275 + -0.275 = 0.000
0.000 + x = 1.060954759 + -0.275
x = 1.060954759 + -0.275

Combine like terms: 1.060954759 + -0.275 = 0.785954759
x = 0.785954759

Simplifying
x = 0.785954759

Subproblem 2
x + 0.275 = -1.060954759

Simplifying
x + 0.275 = -1.060954759

Reorder the terms:
0.275 + x = -1.060954759

Solving
0.275 + x = -1.060954759

Solving for variable 'x'.

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

Add '-0.275' to each side of the equation.
0.275 + -0.275 + x = -1.060954759 + -0.275

Combine like terms: 0.275 + -0.275 = 0.000
0.000 + x = -1.060954759 + -0.275
x = -1.060954759 + -0.275

Combine like terms: -1.060954759 + -0.275 = -1.335954759
x = -1.335954759

Simplifying
x = -1.335954759

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.785954759, -1.335954759}