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

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


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

Reorder the terms:
4x + (2 + 3x)(x + -5) = 0

Reorder the terms:
4x + (2 + 3x)(-5 + x) = 0

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

Combine like terms: 2x + -15x = -13x
4x + (-10 + -13x + 3x2) = 0

Reorder the terms:
-10 + 4x + -13x + 3x2 = 0

Combine like terms: 4x + -13x = -9x
-10 + -9x + 3x2 = 0

Solving
-10 + -9x + 3x2 = 0

Solving for variable 'x'.

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

Divide each side by '3'.
-3.333333333 + -3x + x2 = 0

Move the constant term to the right:

Add '3.333333333' to each side of the equation.
-3.333333333 + -3x + 3.333333333 + x2 = 0 + 3.333333333

Reorder the terms:
-3.333333333 + 3.333333333 + -3x + x2 = 0 + 3.333333333

Combine like terms: -3.333333333 + 3.333333333 = 0.000000000
0.000000000 + -3x + x2 = 0 + 3.333333333
-3x + x2 = 0 + 3.333333333

Combine like terms: 0 + 3.333333333 = 3.333333333
-3x + x2 = 3.333333333

The x term is -3x.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3x + 2.25 + x2 = 3.333333333 + 2.25

Reorder the terms:
2.25 + -3x + x2 = 3.333333333 + 2.25

Combine like terms: 3.333333333 + 2.25 = 5.583333333
2.25 + -3x + x2 = 5.583333333

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 5.583333333

Calculate the square root of the right side: 2.362907813

Break this problem into two subproblems by setting 
(x + -1.5) equal to 2.362907813 and -2.362907813.


Subproblem 1
x + -1.5 = 2.362907813

Simplifying
x + -1.5 = 2.362907813

Reorder the terms:
-1.5 + x = 2.362907813

Solving
-1.5 + x = 2.362907813

Solving for variable 'x'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + x = 2.362907813 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = 2.362907813 + 1.5
x = 2.362907813 + 1.5

Combine like terms: 2.362907813 + 1.5 = 3.862907813
x = 3.862907813

Simplifying
x = 3.862907813


Subproblem 2
x + -1.5 = -2.362907813

Simplifying
x + -1.5 = -2.362907813

Reorder the terms:
-1.5 + x = -2.362907813

Solving
-1.5 + x = -2.362907813

Solving for variable 'x'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + x = -2.362907813 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = -2.362907813 + 1.5
x = -2.362907813 + 1.5

Combine like terms: -2.362907813 + 1.5 = -0.862907813
x = -0.862907813

Simplifying
x = -0.862907813


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.862907813, -0.862907813}

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