12x^2-90x+112=0

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Solution for 12x^2-90x+112=0 equation: 


Simplifying
12x2 + -90x + 112 = 0

Reorder the terms:
112 + -90x + 12x2 = 0

Solving
112 + -90x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(56 + -45x + 6x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(56 + -45x + 6x2)' equal to zero and attempt to solve:

Simplifying
56 + -45x + 6x2 = 0

Solving
56 + -45x + 6x2 = 0

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

Divide each side by '6'.
9.333333333 + -7.5x + x2 = 0

Move the constant term to the right:

Add '-9.333333333' to each side of the equation.
9.333333333 + -7.5x + -9.333333333 + x2 = 0 + -9.333333333

Reorder the terms:
9.333333333 + -9.333333333 + -7.5x + x2 = 0 + -9.333333333

Combine like terms: 9.333333333 + -9.333333333 = 0.000000000
0.000000000 + -7.5x + x2 = 0 + -9.333333333
-7.5x + x2 = 0 + -9.333333333

Combine like terms: 0 + -9.333333333 = -9.333333333
-7.5x + x2 = -9.333333333

The x term is -7.5x.  Take half its coefficient (-3.75).
Square it (14.0625) and add it to both sides.

Add '14.0625' to each side of the equation.
-7.5x + 14.0625 + x2 = -9.333333333 + 14.0625

Reorder the terms:
14.0625 + -7.5x + x2 = -9.333333333 + 14.0625

Combine like terms: -9.333333333 + 14.0625 = 4.729166667
14.0625 + -7.5x + x2 = 4.729166667

Factor a perfect square on the left side:
(x + -3.75)(x + -3.75) = 4.729166667

Calculate the square root of the right side: 2.174664725

Break this problem into two subproblems by setting 
(x + -3.75) equal to 2.174664725 and -2.174664725.


Subproblem 1
x + -3.75 = 2.174664725

Simplifying
x + -3.75 = 2.174664725

Reorder the terms:
-3.75 + x = 2.174664725

Solving
-3.75 + x = 2.174664725

Solving for variable 'x'.

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

Add '3.75' to each side of the equation.
-3.75 + 3.75 + x = 2.174664725 + 3.75

Combine like terms: -3.75 + 3.75 = 0.00
0.00 + x = 2.174664725 + 3.75
x = 2.174664725 + 3.75

Combine like terms: 2.174664725 + 3.75 = 5.924664725
x = 5.924664725

Simplifying
x = 5.924664725


Subproblem 2
x + -3.75 = -2.174664725

Simplifying
x + -3.75 = -2.174664725

Reorder the terms:
-3.75 + x = -2.174664725

Solving
-3.75 + x = -2.174664725

Solving for variable 'x'.

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

Add '3.75' to each side of the equation.
-3.75 + 3.75 + x = -2.174664725 + 3.75

Combine like terms: -3.75 + 3.75 = 0.00
0.00 + x = -2.174664725 + 3.75
x = -2.174664725 + 3.75

Combine like terms: -2.174664725 + 3.75 = 1.575335275
x = 1.575335275

Simplifying
x = 1.575335275


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.924664725, 1.575335275}
Solution
x = {5.924664725, 1.575335275}

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