105=(150-25x)x

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Solution for 105=(150-25x)x equation: 


Simplifying
105 = (150 + -25x) * x

Reorder the terms for easier multiplication:
105 = x(150 + -25x)
105 = (150 * x + -25x * x)
105 = (150x + -25x2)

Solving
105 = 150x + -25x2

Solving for variable 'x'.

Reorder the terms:
105 + -150x + 25x2 = 150x + -150x + -25x2 + 25x2

Combine like terms: 150x + -150x = 0
105 + -150x + 25x2 = 0 + -25x2 + 25x2
105 + -150x + 25x2 = -25x2 + 25x2

Combine like terms: -25x2 + 25x2 = 0
105 + -150x + 25x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(21 + -30x + 5x2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(21 + -30x + 5x2)' equal to zero and attempt to solve:

Simplifying
21 + -30x + 5x2 = 0

Solving
21 + -30x + 5x2 = 0

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

Divide each side by '5'.
4.2 + -6x + x2 = 0

Move the constant term to the right:

Add '-4.2' to each side of the equation.
4.2 + -6x + -4.2 + x2 = 0 + -4.2

Reorder the terms:
4.2 + -4.2 + -6x + x2 = 0 + -4.2

Combine like terms: 4.2 + -4.2 = 0.0
0.0 + -6x + x2 = 0 + -4.2
-6x + x2 = 0 + -4.2

Combine like terms: 0 + -4.2 = -4.2
-6x + x2 = -4.2

The x term is -6x.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6x + 9 + x2 = -4.2 + 9

Reorder the terms:
9 + -6x + x2 = -4.2 + 9

Combine like terms: -4.2 + 9 = 4.8
9 + -6x + x2 = 4.8

Factor a perfect square on the left side:
(x + -3)(x + -3) = 4.8

Calculate the square root of the right side: 2.19089023

Break this problem into two subproblems by setting 
(x + -3) equal to 2.19089023 and -2.19089023.


Subproblem 1
x + -3 = 2.19089023

Simplifying
x + -3 = 2.19089023

Reorder the terms:
-3 + x = 2.19089023

Solving
-3 + x = 2.19089023

Solving for variable 'x'.

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

Add '3' to each side of the equation.
-3 + 3 + x = 2.19089023 + 3

Combine like terms: -3 + 3 = 0
0 + x = 2.19089023 + 3
x = 2.19089023 + 3

Combine like terms: 2.19089023 + 3 = 5.19089023
x = 5.19089023

Simplifying
x = 5.19089023


Subproblem 2
x + -3 = -2.19089023

Simplifying
x + -3 = -2.19089023

Reorder the terms:
-3 + x = -2.19089023

Solving
-3 + x = -2.19089023

Solving for variable 'x'.

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

Add '3' to each side of the equation.
-3 + 3 + x = -2.19089023 + 3

Combine like terms: -3 + 3 = 0
0 + x = -2.19089023 + 3
x = -2.19089023 + 3

Combine like terms: -2.19089023 + 3 = 0.80910977
x = 0.80910977

Simplifying
x = 0.80910977


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.19089023, 0.80910977}
Solution
x = {5.19089023, 0.80910977}

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