12x^2-42x-24=10

Solution for 12x^2-42x-24=10 equation:

Simplifying
12x2 + -42x + -24 = 10

Reorder the terms:
-24 + -42x + 12x2 = 10

Solving
-24 + -42x + 12x2 = 10

Solving for variable 'x'.

Reorder the terms:
-24 + -10 + -42x + 12x2 = 10 + -10

Combine like terms: -24 + -10 = -34
-34 + -42x + 12x2 = 10 + -10

Combine like terms: 10 + -10 = 0
-34 + -42x + 12x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-17 + -21x + 6x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-17 + -21x + 6x2)' equal to zero and attempt to solve:

Simplifying
-17 + -21x + 6x2 = 0

Solving
-17 + -21x + 6x2 = 0

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

Divide each side by '6'.
-2.833333333 + -3.5x + x2 = 0

Move the constant term to the right:

Add '2.833333333' to each side of the equation.
-2.833333333 + -3.5x + 2.833333333 + x2 = 0 + 2.833333333

Reorder the terms:
-2.833333333 + 2.833333333 + -3.5x + x2 = 0 + 2.833333333

Combine like terms: -2.833333333 + 2.833333333 = 0.000000000
0.000000000 + -3.5x + x2 = 0 + 2.833333333
-3.5x + x2 = 0 + 2.833333333

Combine like terms: 0 + 2.833333333 = 2.833333333
-3.5x + x2 = 2.833333333

The x term is -3.5x.  Take half its coefficient (-1.75).
Square it (3.0625) and add it to both sides.

Add '3.0625' to each side of the equation.
-3.5x + 3.0625 + x2 = 2.833333333 + 3.0625

Reorder the terms:
3.0625 + -3.5x + x2 = 2.833333333 + 3.0625

Combine like terms: 2.833333333 + 3.0625 = 5.895833333
3.0625 + -3.5x + x2 = 5.895833333

Factor a perfect square on the left side:
(x + -1.75)(x + -1.75) = 5.895833333

Calculate the square root of the right side: 2.428133714

Break this problem into two subproblems by setting 
(x + -1.75) equal to 2.428133714 and -2.428133714.

Subproblem 1
x + -1.75 = 2.428133714

Simplifying
x + -1.75 = 2.428133714

Reorder the terms:
-1.75 + x = 2.428133714

Solving
-1.75 + x = 2.428133714

Solving for variable 'x'.

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

Add '1.75' to each side of the equation.
-1.75 + 1.75 + x = 2.428133714 + 1.75

Combine like terms: -1.75 + 1.75 = 0.00
0.00 + x = 2.428133714 + 1.75
x = 2.428133714 + 1.75

Combine like terms: 2.428133714 + 1.75 = 4.178133714
x = 4.178133714

Simplifying
x = 4.178133714

Subproblem 2
x + -1.75 = -2.428133714

Simplifying
x + -1.75 = -2.428133714

Reorder the terms:
-1.75 + x = -2.428133714

Solving
-1.75 + x = -2.428133714

Solving for variable 'x'.

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

Add '1.75' to each side of the equation.
-1.75 + 1.75 + x = -2.428133714 + 1.75

Combine like terms: -1.75 + 1.75 = 0.00
0.00 + x = -2.428133714 + 1.75
x = -2.428133714 + 1.75

Combine like terms: -2.428133714 + 1.75 = -0.678133714
x = -0.678133714

Simplifying
x = -0.678133714

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.178133714, -0.678133714}
Solution
x = {4.178133714, -0.678133714}