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

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


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

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

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

Multiply (2 + 4x) * (-5 + x)
(2(-5 + x) + 4x * (-5 + x)) + 3 = 0
((-5 * 2 + x * 2) + 4x * (-5 + x)) + 3 = 0
((-10 + 2x) + 4x * (-5 + x)) + 3 = 0
(-10 + 2x + (-5 * 4x + x * 4x)) + 3 = 0
(-10 + 2x + (-20x + 4x2)) + 3 = 0

Combine like terms: 2x + -20x = -18x
(-10 + -18x + 4x2) + 3 = 0

Reorder the terms:
-10 + 3 + -18x + 4x2 = 0

Combine like terms: -10 + 3 = -7
-7 + -18x + 4x2 = 0

Solving
-7 + -18x + 4x2 = 0

Solving for variable 'x'.

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

Divide each side by '4'.
-1.75 + -4.5x + x2 = 0

Move the constant term to the right:

Add '1.75' to each side of the equation.
-1.75 + -4.5x + 1.75 + x2 = 0 + 1.75

Reorder the terms:
-1.75 + 1.75 + -4.5x + x2 = 0 + 1.75

Combine like terms: -1.75 + 1.75 = 0.00
0.00 + -4.5x + x2 = 0 + 1.75
-4.5x + x2 = 0 + 1.75

Combine like terms: 0 + 1.75 = 1.75
-4.5x + x2 = 1.75

The x term is -4.5x.  Take half its coefficient (-2.25).
Square it (5.0625) and add it to both sides.

Add '5.0625' to each side of the equation.
-4.5x + 5.0625 + x2 = 1.75 + 5.0625

Reorder the terms:
5.0625 + -4.5x + x2 = 1.75 + 5.0625

Combine like terms: 1.75 + 5.0625 = 6.8125
5.0625 + -4.5x + x2 = 6.8125

Factor a perfect square on the left side:
(x + -2.25)(x + -2.25) = 6.8125

Calculate the square root of the right side: 2.610076627

Break this problem into two subproblems by setting 
(x + -2.25) equal to 2.610076627 and -2.610076627.


Subproblem 1
x + -2.25 = 2.610076627

Simplifying
x + -2.25 = 2.610076627

Reorder the terms:
-2.25 + x = 2.610076627

Solving
-2.25 + x = 2.610076627

Solving for variable 'x'.

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

Add '2.25' to each side of the equation.
-2.25 + 2.25 + x = 2.610076627 + 2.25

Combine like terms: -2.25 + 2.25 = 0.00
0.00 + x = 2.610076627 + 2.25
x = 2.610076627 + 2.25

Combine like terms: 2.610076627 + 2.25 = 4.860076627
x = 4.860076627

Simplifying
x = 4.860076627


Subproblem 2
x + -2.25 = -2.610076627

Simplifying
x + -2.25 = -2.610076627

Reorder the terms:
-2.25 + x = -2.610076627

Solving
-2.25 + x = -2.610076627

Solving for variable 'x'.

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

Add '2.25' to each side of the equation.
-2.25 + 2.25 + x = -2.610076627 + 2.25

Combine like terms: -2.25 + 2.25 = 0.00
0.00 + x = -2.610076627 + 2.25
x = -2.610076627 + 2.25

Combine like terms: -2.610076627 + 2.25 = -0.360076627
x = -0.360076627

Simplifying
x = -0.360076627


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.860076627, -0.360076627}

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