5x+(3-2x)(2+5x)+4=

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

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

Multiply (3 + -2x) * (2 + 5x)
5x + (3(2 + 5x) + -2x * (2 + 5x)) + 4 = 0
5x + ((2 * 3 + 5x * 3) + -2x * (2 + 5x)) + 4 = 0
5x + ((6 + 15x) + -2x * (2 + 5x)) + 4 = 0
5x + (6 + 15x + (2 * -2x + 5x * -2x)) + 4 = 0
5x + (6 + 15x + (-4x + -10x2)) + 4 = 0

Combine like terms: 15x + -4x = 11x
5x + (6 + 11x + -10x2) + 4 = 0

Reorder the terms:
6 + 4 + 5x + 11x + -10x2 = 0

Combine like terms: 6 + 4 = 10
10 + 5x + 11x + -10x2 = 0

Combine like terms: 5x + 11x = 16x
10 + 16x + -10x2 = 0

Solving
10 + 16x + -10x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(5 + 8x + -5x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(5 + 8x + -5x2)' equal to zero and attempt to solve:

Simplifying
5 + 8x + -5x2 = 0

Solving
5 + 8x + -5x2 = 0

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

Divide each side by '-5'.
-1 + -1.6x + x2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -1.6x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + -1.6x + x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -1.6x + x2 = 0 + 1
-1.6x + x2 = 0 + 1

Combine like terms: 0 + 1 = 1
-1.6x + x2 = 1

The x term is -1.6x.  Take half its coefficient (-0.8).
Square it (0.64) and add it to both sides.

Add '0.64' to each side of the equation.
-1.6x + 0.64 + x2 = 1 + 0.64

Reorder the terms:
0.64 + -1.6x + x2 = 1 + 0.64

Combine like terms: 1 + 0.64 = 1.64
0.64 + -1.6x + x2 = 1.64

Factor a perfect square on the left side:
(x + -0.8)(x + -0.8) = 1.64

Calculate the square root of the right side: 1.280624847

Break this problem into two subproblems by setting 
(x + -0.8) equal to 1.280624847 and -1.280624847.

Subproblem 1
x + -0.8 = 1.280624847

Simplifying
x + -0.8 = 1.280624847

Reorder the terms:
-0.8 + x = 1.280624847

Solving
-0.8 + x = 1.280624847

Solving for variable 'x'.

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

Add '0.8' to each side of the equation.
-0.8 + 0.8 + x = 1.280624847 + 0.8

Combine like terms: -0.8 + 0.8 = 0.0
0.0 + x = 1.280624847 + 0.8
x = 1.280624847 + 0.8

Combine like terms: 1.280624847 + 0.8 = 2.080624847
x = 2.080624847

Simplifying
x = 2.080624847

Subproblem 2
x + -0.8 = -1.280624847

Simplifying
x + -0.8 = -1.280624847

Reorder the terms:
-0.8 + x = -1.280624847

Solving
-0.8 + x = -1.280624847

Solving for variable 'x'.

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

Add '0.8' to each side of the equation.
-0.8 + 0.8 + x = -1.280624847 + 0.8

Combine like terms: -0.8 + 0.8 = 0.0
0.0 + x = -1.280624847 + 0.8
x = -1.280624847 + 0.8

Combine like terms: -1.280624847 + 0.8 = -0.480624847
x = -0.480624847

Simplifying
x = -0.480624847

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.080624847, -0.480624847}
Solution
x = {2.080624847, -0.480624847}