10x^2=24x+12

Solution for 10x^2=24x+12 equation:

Simplifying
10x2 = 24x + 12

Reorder the terms:
10x2 = 12 + 24x

Solving
10x2 = 12 + 24x

Solving for variable 'x'.

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

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

Combine like terms: 12 + -12 = 0
-12 + -24x + 10x2 = 0 + 24x + -24x
-12 + -24x + 10x2 = 24x + -24x

Combine like terms: 24x + -24x = 0
-12 + -24x + 10x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-6 + -12x + 5x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-6 + -12x + 5x2)' equal to zero and attempt to solve:

Simplifying
-6 + -12x + 5x2 = 0

Solving
-6 + -12x + 5x2 = 0

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

Divide each side by '5'.
-1.2 + -2.4x + x2 = 0

Move the constant term to the right:

Add '1.2' to each side of the equation.
-1.2 + -2.4x + 1.2 + x2 = 0 + 1.2

Reorder the terms:
-1.2 + 1.2 + -2.4x + x2 = 0 + 1.2

Combine like terms: -1.2 + 1.2 = 0.0
0.0 + -2.4x + x2 = 0 + 1.2
-2.4x + x2 = 0 + 1.2

Combine like terms: 0 + 1.2 = 1.2
-2.4x + x2 = 1.2

The x term is -2.4x.  Take half its coefficient (-1.2).
Square it (1.44) and add it to both sides.

Add '1.44' to each side of the equation.
-2.4x + 1.44 + x2 = 1.2 + 1.44

Reorder the terms:
1.44 + -2.4x + x2 = 1.2 + 1.44

Combine like terms: 1.2 + 1.44 = 2.64
1.44 + -2.4x + x2 = 2.64

Factor a perfect square on the left side:
(x + -1.2)(x + -1.2) = 2.64

Calculate the square root of the right side: 1.624807681

Break this problem into two subproblems by setting 
(x + -1.2) equal to 1.624807681 and -1.624807681.

Subproblem 1
x + -1.2 = 1.624807681

Simplifying
x + -1.2 = 1.624807681

Reorder the terms:
-1.2 + x = 1.624807681

Solving
-1.2 + x = 1.624807681

Solving for variable 'x'.

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

Add '1.2' to each side of the equation.
-1.2 + 1.2 + x = 1.624807681 + 1.2

Combine like terms: -1.2 + 1.2 = 0.0
0.0 + x = 1.624807681 + 1.2
x = 1.624807681 + 1.2

Combine like terms: 1.624807681 + 1.2 = 2.824807681
x = 2.824807681

Simplifying
x = 2.824807681

Subproblem 2
x + -1.2 = -1.624807681

Simplifying
x + -1.2 = -1.624807681

Reorder the terms:
-1.2 + x = -1.624807681

Solving
-1.2 + x = -1.624807681

Solving for variable 'x'.

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

Add '1.2' to each side of the equation.
-1.2 + 1.2 + x = -1.624807681 + 1.2

Combine like terms: -1.2 + 1.2 = 0.0
0.0 + x = -1.624807681 + 1.2
x = -1.624807681 + 1.2

Combine like terms: -1.624807681 + 1.2 = -0.424807681
x = -0.424807681

Simplifying
x = -0.424807681

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.824807681, -0.424807681}
Solution
x = {2.824807681, -0.424807681}