(4-0.25x)(6+x)=30

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Solution for (4-0.25x)(6+x)=30 equation: 


Simplifying
(4 + -0.25x)(6 + x) = 30

Multiply (4 + -0.25x) * (6 + x)
(4(6 + x) + -0.25x * (6 + x)) = 30
((6 * 4 + x * 4) + -0.25x * (6 + x)) = 30
((24 + 4x) + -0.25x * (6 + x)) = 30
(24 + 4x + (6 * -0.25x + x * -0.25x)) = 30
(24 + 4x + (-1.5x + -0.25x2)) = 30

Combine like terms: 4x + -1.5x = 2.5x
(24 + 2.5x + -0.25x2) = 30

Solving
24 + 2.5x + -0.25x2 = 30

Solving for variable 'x'.

Reorder the terms:
24 + -30 + 2.5x + -0.25x2 = 30 + -30

Combine like terms: 24 + -30 = -6
-6 + 2.5x + -0.25x2 = 30 + -30

Combine like terms: 30 + -30 = 0
-6 + 2.5x + -0.25x2 = 0

Begin completing the square.  Divide all terms by
-0.25 the coefficient of the squared term: 

Divide each side by '-0.25'.
24 + -10x + x2 = 0

Move the constant term to the right:

Add '-24' to each side of the equation.
24 + -10x + -24 + x2 = 0 + -24

Reorder the terms:
24 + -24 + -10x + x2 = 0 + -24

Combine like terms: 24 + -24 = 0
0 + -10x + x2 = 0 + -24
-10x + x2 = 0 + -24

Combine like terms: 0 + -24 = -24
-10x + x2 = -24

The x term is -10x.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10x + 25 + x2 = -24 + 25

Reorder the terms:
25 + -10x + x2 = -24 + 25

Combine like terms: -24 + 25 = 1
25 + -10x + x2 = 1

Factor a perfect square on the left side:
(x + -5)(x + -5) = 1

Calculate the square root of the right side: 1

Break this problem into two subproblems by setting 
(x + -5) equal to 1 and -1.


Subproblem 1
x + -5 = 1

Simplifying
x + -5 = 1

Reorder the terms:
-5 + x = 1

Solving
-5 + x = 1

Solving for variable 'x'.

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

Add '5' to each side of the equation.
-5 + 5 + x = 1 + 5

Combine like terms: -5 + 5 = 0
0 + x = 1 + 5
x = 1 + 5

Combine like terms: 1 + 5 = 6
x = 6

Simplifying
x = 6


Subproblem 2
x + -5 = -1

Simplifying
x + -5 = -1

Reorder the terms:
-5 + x = -1

Solving
-5 + x = -1

Solving for variable 'x'.

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

Add '5' to each side of the equation.
-5 + 5 + x = -1 + 5

Combine like terms: -5 + 5 = 0
0 + x = -1 + 5
x = -1 + 5

Combine like terms: -1 + 5 = 4
x = 4

Simplifying
x = 4


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6, 4}

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