4x(x+1)-10(x+3)=4

Solution for 4x(x+1)-10(x+3)=4 equation:

Simplifying
4x(x + 1) + -10(x + 3) = 4

Reorder the terms:
4x(1 + x) + -10(x + 3) = 4
(1 * 4x + x * 4x) + -10(x + 3) = 4
(4x + 4x2) + -10(x + 3) = 4

Reorder the terms:
4x + 4x2 + -10(3 + x) = 4
4x + 4x2 + (3 * -10 + x * -10) = 4
4x + 4x2 + (-30 + -10x) = 4

Reorder the terms:
-30 + 4x + -10x + 4x2 = 4

Combine like terms: 4x + -10x = -6x
-30 + -6x + 4x2 = 4

Solving
-30 + -6x + 4x2 = 4

Solving for variable 'x'.

Reorder the terms:
-30 + -4 + -6x + 4x2 = 4 + -4

Combine like terms: -30 + -4 = -34
-34 + -6x + 4x2 = 4 + -4

Combine like terms: 4 + -4 = 0
-34 + -6x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-17 + -3x + 2x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-17 + -3x + 2x2)' equal to zero and attempt to solve:

Simplifying
-17 + -3x + 2x2 = 0

Solving
-17 + -3x + 2x2 = 0

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

Divide each side by '2'.
-8.5 + -1.5x + x2 = 0

Move the constant term to the right:

Add '8.5' to each side of the equation.
-8.5 + -1.5x + 8.5 + x2 = 0 + 8.5

Reorder the terms:
-8.5 + 8.5 + -1.5x + x2 = 0 + 8.5

Combine like terms: -8.5 + 8.5 = 0.0
0.0 + -1.5x + x2 = 0 + 8.5
-1.5x + x2 = 0 + 8.5

Combine like terms: 0 + 8.5 = 8.5
-1.5x + x2 = 8.5

The x term is -1.5x.  Take half its coefficient (-0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
-1.5x + 0.5625 + x2 = 8.5 + 0.5625

Reorder the terms:
0.5625 + -1.5x + x2 = 8.5 + 0.5625

Combine like terms: 8.5 + 0.5625 = 9.0625
0.5625 + -1.5x + x2 = 9.0625

Factor a perfect square on the left side:
(x + -0.75)(x + -0.75) = 9.0625

Calculate the square root of the right side: 3.010398645

Break this problem into two subproblems by setting 
(x + -0.75) equal to 3.010398645 and -3.010398645.

Subproblem 1
x + -0.75 = 3.010398645

Simplifying
x + -0.75 = 3.010398645

Reorder the terms:
-0.75 + x = 3.010398645

Solving
-0.75 + x = 3.010398645

Solving for variable 'x'.

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

Add '0.75' to each side of the equation.
-0.75 + 0.75 + x = 3.010398645 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + x = 3.010398645 + 0.75
x = 3.010398645 + 0.75

Combine like terms: 3.010398645 + 0.75 = 3.760398645
x = 3.760398645

Simplifying
x = 3.760398645

Subproblem 2
x + -0.75 = -3.010398645

Simplifying
x + -0.75 = -3.010398645

Reorder the terms:
-0.75 + x = -3.010398645

Solving
-0.75 + x = -3.010398645

Solving for variable 'x'.

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

Add '0.75' to each side of the equation.
-0.75 + 0.75 + x = -3.010398645 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + x = -3.010398645 + 0.75
x = -3.010398645 + 0.75

Combine like terms: -3.010398645 + 0.75 = -2.260398645
x = -2.260398645

Simplifying
x = -2.260398645

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.760398645, -2.260398645}
Solution
x = {3.760398645, -2.260398645}