42x^2+24x-5=5

Solution for 42x^2+24x-5=5 equation:

Simplifying
42x2 + 24x + -5 = 5

Reorder the terms:
-5 + 24x + 42x2 = 5

Solving
-5 + 24x + 42x2 = 5

Solving for variable 'x'.

Reorder the terms:
-5 + -5 + 24x + 42x2 = 5 + -5

Combine like terms: -5 + -5 = -10
-10 + 24x + 42x2 = 5 + -5

Combine like terms: 5 + -5 = 0
-10 + 24x + 42x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + 12x + 21x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-5 + 12x + 21x2)' equal to zero and attempt to solve:

Simplifying
-5 + 12x + 21x2 = 0

Solving
-5 + 12x + 21x2 = 0

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

Divide each side by '21'.
-0.2380952381 + 0.5714285714x + x2 = 0

Move the constant term to the right:

Add '0.2380952381' to each side of the equation.
-0.2380952381 + 0.5714285714x + 0.2380952381 + x2 = 0 + 0.2380952381

Reorder the terms:
-0.2380952381 + 0.2380952381 + 0.5714285714x + x2 = 0 + 0.2380952381

Combine like terms: -0.2380952381 + 0.2380952381 = 0.0000000000
0.0000000000 + 0.5714285714x + x2 = 0 + 0.2380952381
0.5714285714x + x2 = 0 + 0.2380952381

Combine like terms: 0 + 0.2380952381 = 0.2380952381
0.5714285714x + x2 = 0.2380952381

The x term is 0.5714285714x.  Take half its coefficient (0.2857142857).
Square it (0.08163265305) and add it to both sides.

Add '0.08163265305' to each side of the equation.
0.5714285714x + 0.08163265305 + x2 = 0.2380952381 + 0.08163265305

Reorder the terms:
0.08163265305 + 0.5714285714x + x2 = 0.2380952381 + 0.08163265305

Combine like terms: 0.2380952381 + 0.08163265305 = 0.31972789115
0.08163265305 + 0.5714285714x + x2 = 0.31972789115

Factor a perfect square on the left side:
(x + 0.2857142857)(x + 0.2857142857) = 0.31972789115

Calculate the square root of the right side: 0.565444861

Break this problem into two subproblems by setting 
(x + 0.2857142857) equal to 0.565444861 and -0.565444861.

Subproblem 1
x + 0.2857142857 = 0.565444861

Simplifying
x + 0.2857142857 = 0.565444861

Reorder the terms:
0.2857142857 + x = 0.565444861

Solving
0.2857142857 + x = 0.565444861

Solving for variable 'x'.

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

Add '-0.2857142857' to each side of the equation.
0.2857142857 + -0.2857142857 + x = 0.565444861 + -0.2857142857

Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000
0.0000000000 + x = 0.565444861 + -0.2857142857
x = 0.565444861 + -0.2857142857

Combine like terms: 0.565444861 + -0.2857142857 = 0.2797305753
x = 0.2797305753

Simplifying
x = 0.2797305753

Subproblem 2
x + 0.2857142857 = -0.565444861

Simplifying
x + 0.2857142857 = -0.565444861

Reorder the terms:
0.2857142857 + x = -0.565444861

Solving
0.2857142857 + x = -0.565444861

Solving for variable 'x'.

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

Add '-0.2857142857' to each side of the equation.
0.2857142857 + -0.2857142857 + x = -0.565444861 + -0.2857142857

Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000
0.0000000000 + x = -0.565444861 + -0.2857142857
x = -0.565444861 + -0.2857142857

Combine like terms: -0.565444861 + -0.2857142857 = -0.8511591467
x = -0.8511591467

Simplifying
x = -0.8511591467

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.2797305753, -0.8511591467}
Solution
x = {0.2797305753, -0.8511591467}