2x(4x-1)+5(x+1)(x-3)=

Solution for 2x(4x-1)+5(x+1)(x-3)= equation:

Simplifying
2x(4x + -1) + 5(x + 1)(x + -3) = 0

Reorder the terms:
2x(-1 + 4x) + 5(x + 1)(x + -3) = 0
(-1 * 2x + 4x * 2x) + 5(x + 1)(x + -3) = 0
(-2x + 8x2) + 5(x + 1)(x + -3) = 0

Reorder the terms:
-2x + 8x2 + 5(1 + x)(x + -3) = 0

Reorder the terms:
-2x + 8x2 + 5(1 + x)(-3 + x) = 0

Multiply (1 + x) * (-3 + x)
-2x + 8x2 + 5(1(-3 + x) + x(-3 + x)) = 0
-2x + 8x2 + 5((-3 * 1 + x * 1) + x(-3 + x)) = 0
-2x + 8x2 + 5((-3 + 1x) + x(-3 + x)) = 0
-2x + 8x2 + 5(-3 + 1x + (-3 * x + x * x)) = 0
-2x + 8x2 + 5(-3 + 1x + (-3x + x2)) = 0

Combine like terms: 1x + -3x = -2x
-2x + 8x2 + 5(-3 + -2x + x2) = 0
-2x + 8x2 + (-3 * 5 + -2x * 5 + x2 * 5) = 0
-2x + 8x2 + (-15 + -10x + 5x2) = 0

Reorder the terms:
-15 + -2x + -10x + 8x2 + 5x2 = 0

Combine like terms: -2x + -10x = -12x
-15 + -12x + 8x2 + 5x2 = 0

Combine like terms: 8x2 + 5x2 = 13x2
-15 + -12x + 13x2 = 0

Solving
-15 + -12x + 13x2 = 0

Solving for variable 'x'.

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

Divide each side by '13'.
-1.153846154 + -0.9230769231x + x2 = 0

Move the constant term to the right:

Add '1.153846154' to each side of the equation.
-1.153846154 + -0.9230769231x + 1.153846154 + x2 = 0 + 1.153846154

Reorder the terms:
-1.153846154 + 1.153846154 + -0.9230769231x + x2 = 0 + 1.153846154

Combine like terms: -1.153846154 + 1.153846154 = 0.000000000
0.000000000 + -0.9230769231x + x2 = 0 + 1.153846154
-0.9230769231x + x2 = 0 + 1.153846154

Combine like terms: 0 + 1.153846154 = 1.153846154
-0.9230769231x + x2 = 1.153846154

The x term is -0.9230769231x.  Take half its coefficient (-0.4615384616).
Square it (0.2130177515) and add it to both sides.

Add '0.2130177515' to each side of the equation.
-0.9230769231x + 0.2130177515 + x2 = 1.153846154 + 0.2130177515

Reorder the terms:
0.2130177515 + -0.9230769231x + x2 = 1.153846154 + 0.2130177515

Combine like terms: 1.153846154 + 0.2130177515 = 1.3668639055
0.2130177515 + -0.9230769231x + x2 = 1.3668639055

Factor a perfect square on the left side:
(x + -0.4615384616)(x + -0.4615384616) = 1.3668639055

Calculate the square root of the right side: 1.16912955

Break this problem into two subproblems by setting 
(x + -0.4615384616) equal to 1.16912955 and -1.16912955.

Subproblem 1
x + -0.4615384616 = 1.16912955

Simplifying
x + -0.4615384616 = 1.16912955

Reorder the terms:
-0.4615384616 + x = 1.16912955

Solving
-0.4615384616 + x = 1.16912955

Solving for variable 'x'.

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

Add '0.4615384616' to each side of the equation.
-0.4615384616 + 0.4615384616 + x = 1.16912955 + 0.4615384616

Combine like terms: -0.4615384616 + 0.4615384616 = 0.0000000000
0.0000000000 + x = 1.16912955 + 0.4615384616
x = 1.16912955 + 0.4615384616

Combine like terms: 1.16912955 + 0.4615384616 = 1.6306680116
x = 1.6306680116

Simplifying
x = 1.6306680116

Subproblem 2
x + -0.4615384616 = -1.16912955

Simplifying
x + -0.4615384616 = -1.16912955

Reorder the terms:
-0.4615384616 + x = -1.16912955

Solving
-0.4615384616 + x = -1.16912955

Solving for variable 'x'.

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

Add '0.4615384616' to each side of the equation.
-0.4615384616 + 0.4615384616 + x = -1.16912955 + 0.4615384616

Combine like terms: -0.4615384616 + 0.4615384616 = 0.0000000000
0.0000000000 + x = -1.16912955 + 0.4615384616
x = -1.16912955 + 0.4615384616

Combine like terms: -1.16912955 + 0.4615384616 = -0.7075910884
x = -0.7075910884

Simplifying
x = -0.7075910884

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.6306680116, -0.7075910884}