(x-7)(3x)=120

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Solution for (x-7)(3x)=120 equation: 


Simplifying
(x + -7)(3x) = 120

Reorder the terms:
(-7 + x)(3x) = 120

Remove parenthesis around (3x)
(-7 + x) * 3x = 120

Reorder the terms for easier multiplication:
3x(-7 + x) = 120
(-7 * 3x + x * 3x) = 120
(-21x + 3x2) = 120

Solving
-21x + 3x2 = 120

Solving for variable 'x'.

Reorder the terms:
-120 + -21x + 3x2 = 120 + -120

Combine like terms: 120 + -120 = 0
-120 + -21x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-40 + -7x + x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-40 + -7x + x2)' equal to zero and attempt to solve:

Simplifying
-40 + -7x + x2 = 0

Solving
-40 + -7x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '40' to each side of the equation.
-40 + -7x + 40 + x2 = 0 + 40

Reorder the terms:
-40 + 40 + -7x + x2 = 0 + 40

Combine like terms: -40 + 40 = 0
0 + -7x + x2 = 0 + 40
-7x + x2 = 0 + 40

Combine like terms: 0 + 40 = 40
-7x + x2 = 40

The x term is -7x.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7x + 12.25 + x2 = 40 + 12.25

Reorder the terms:
12.25 + -7x + x2 = 40 + 12.25

Combine like terms: 40 + 12.25 = 52.25
12.25 + -7x + x2 = 52.25

Factor a perfect square on the left side:
(x + -3.5)(x + -3.5) = 52.25

Calculate the square root of the right side: 7.228416147

Break this problem into two subproblems by setting 
(x + -3.5) equal to 7.228416147 and -7.228416147.


Subproblem 1
x + -3.5 = 7.228416147

Simplifying
x + -3.5 = 7.228416147

Reorder the terms:
-3.5 + x = 7.228416147

Solving
-3.5 + x = 7.228416147

Solving for variable 'x'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + x = 7.228416147 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + x = 7.228416147 + 3.5
x = 7.228416147 + 3.5

Combine like terms: 7.228416147 + 3.5 = 10.728416147
x = 10.728416147

Simplifying
x = 10.728416147


Subproblem 2
x + -3.5 = -7.228416147

Simplifying
x + -3.5 = -7.228416147

Reorder the terms:
-3.5 + x = -7.228416147

Solving
-3.5 + x = -7.228416147

Solving for variable 'x'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + x = -7.228416147 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + x = -7.228416147 + 3.5
x = -7.228416147 + 3.5

Combine like terms: -7.228416147 + 3.5 = -3.728416147
x = -3.728416147

Simplifying
x = -3.728416147


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.728416147, -3.728416147}
Solution
x = {10.728416147, -3.728416147}

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