4x^2-42x+60=0

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Solution for 4x^2-42x+60=0 equation: 


Simplifying
4x2 + -42x + 60 = 0

Reorder the terms:
60 + -42x + 4x2 = 0

Solving
60 + -42x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(30 + -21x + 2x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(30 + -21x + 2x2)' equal to zero and attempt to solve:

Simplifying
30 + -21x + 2x2 = 0

Solving
30 + -21x + 2x2 = 0

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

Divide each side by '2'.
15 + -10.5x + x2 = 0

Move the constant term to the right:

Add '-15' to each side of the equation.
15 + -10.5x + -15 + x2 = 0 + -15

Reorder the terms:
15 + -15 + -10.5x + x2 = 0 + -15

Combine like terms: 15 + -15 = 0
0 + -10.5x + x2 = 0 + -15
-10.5x + x2 = 0 + -15

Combine like terms: 0 + -15 = -15
-10.5x + x2 = -15

The x term is -10.5x.  Take half its coefficient (-5.25).
Square it (27.5625) and add it to both sides.

Add '27.5625' to each side of the equation.
-10.5x + 27.5625 + x2 = -15 + 27.5625

Reorder the terms:
27.5625 + -10.5x + x2 = -15 + 27.5625

Combine like terms: -15 + 27.5625 = 12.5625
27.5625 + -10.5x + x2 = 12.5625

Factor a perfect square on the left side:
(x + -5.25)(x + -5.25) = 12.5625

Calculate the square root of the right side: 3.54436172

Break this problem into two subproblems by setting 
(x + -5.25) equal to 3.54436172 and -3.54436172.


Subproblem 1
x + -5.25 = 3.54436172

Simplifying
x + -5.25 = 3.54436172

Reorder the terms:
-5.25 + x = 3.54436172

Solving
-5.25 + x = 3.54436172

Solving for variable 'x'.

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

Add '5.25' to each side of the equation.
-5.25 + 5.25 + x = 3.54436172 + 5.25

Combine like terms: -5.25 + 5.25 = 0.00
0.00 + x = 3.54436172 + 5.25
x = 3.54436172 + 5.25

Combine like terms: 3.54436172 + 5.25 = 8.79436172
x = 8.79436172

Simplifying
x = 8.79436172


Subproblem 2
x + -5.25 = -3.54436172

Simplifying
x + -5.25 = -3.54436172

Reorder the terms:
-5.25 + x = -3.54436172

Solving
-5.25 + x = -3.54436172

Solving for variable 'x'.

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

Add '5.25' to each side of the equation.
-5.25 + 5.25 + x = -3.54436172 + 5.25

Combine like terms: -5.25 + 5.25 = 0.00
0.00 + x = -3.54436172 + 5.25
x = -3.54436172 + 5.25

Combine like terms: -3.54436172 + 5.25 = 1.70563828
x = 1.70563828

Simplifying
x = 1.70563828


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.79436172, 1.70563828}
Solution
x = {8.79436172, 1.70563828}

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