(24x)(43x)=8x+42

Solution for (24x)(43x)=8x+42 equation:

Simplifying
(24x)(43x) = 8x + 42

Remove parenthesis around (24x)
24x(43x) = 8x + 42

Remove parenthesis around (43x)
24x * 43x = 8x + 42

Reorder the terms for easier multiplication:
24 * 43x * x = 8x + 42

Multiply 24 * 43
1032x * x = 8x + 42

Multiply x * x
1032x2 = 8x + 42

Reorder the terms:
1032x2 = 42 + 8x

Solving
1032x2 = 42 + 8x

Solving for variable 'x'.

Reorder the terms:
-42 + -8x + 1032x2 = 42 + 8x + -42 + -8x

Reorder the terms:
-42 + -8x + 1032x2 = 42 + -42 + 8x + -8x

Combine like terms: 42 + -42 = 0
-42 + -8x + 1032x2 = 0 + 8x + -8x
-42 + -8x + 1032x2 = 8x + -8x

Combine like terms: 8x + -8x = 0
-42 + -8x + 1032x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-21 + -4x + 516x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-21 + -4x + 516x2)' equal to zero and attempt to solve:

Simplifying
-21 + -4x + 516x2 = 0

Solving
-21 + -4x + 516x2 = 0

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

Divide each side by '516'.
-0.04069767442 + -0.007751937984x + x2 = 0

Move the constant term to the right:

Add '0.04069767442' to each side of the equation.
-0.04069767442 + -0.007751937984x + 0.04069767442 + x2 = 0 + 0.04069767442

Reorder the terms:
-0.04069767442 + 0.04069767442 + -0.007751937984x + x2 = 0 + 0.04069767442

Combine like terms: -0.04069767442 + 0.04069767442 = 0.00000000000
0.00000000000 + -0.007751937984x + x2 = 0 + 0.04069767442
-0.007751937984x + x2 = 0 + 0.04069767442

Combine like terms: 0 + 0.04069767442 = 0.04069767442
-0.007751937984x + x2 = 0.04069767442

The x term is -0.007751937984x.  Take half its coefficient (-0.003875968992).
Square it (0.00001502313563) and add it to both sides.

Add '0.00001502313563' to each side of the equation.
-0.007751937984x + 0.00001502313563 + x2 = 0.04069767442 + 0.00001502313563

Reorder the terms:
0.00001502313563 + -0.007751937984x + x2 = 0.04069767442 + 0.00001502313563

Combine like terms: 0.04069767442 + 0.00001502313563 = 0.04071269755563
0.00001502313563 + -0.007751937984x + x2 = 0.04071269755563

Factor a perfect square on the left side:
(x + -0.003875968992)(x + -0.003875968992) = 0.04071269755563

Calculate the square root of the right side: 0.201773877

Break this problem into two subproblems by setting 
(x + -0.003875968992) equal to 0.201773877 and -0.201773877.

Subproblem 1
x + -0.003875968992 = 0.201773877

Simplifying
x + -0.003875968992 = 0.201773877

Reorder the terms:
-0.003875968992 + x = 0.201773877

Solving
-0.003875968992 + x = 0.201773877

Solving for variable 'x'.

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

Add '0.003875968992' to each side of the equation.
-0.003875968992 + 0.003875968992 + x = 0.201773877 + 0.003875968992

Combine like terms: -0.003875968992 + 0.003875968992 = 0.000000000000
0.000000000000 + x = 0.201773877 + 0.003875968992
x = 0.201773877 + 0.003875968992

Combine like terms: 0.201773877 + 0.003875968992 = 0.205649845992
x = 0.205649845992

Simplifying
x = 0.205649845992

Subproblem 2
x + -0.003875968992 = -0.201773877

Simplifying
x + -0.003875968992 = -0.201773877

Reorder the terms:
-0.003875968992 + x = -0.201773877

Solving
-0.003875968992 + x = -0.201773877

Solving for variable 'x'.

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

Add '0.003875968992' to each side of the equation.
-0.003875968992 + 0.003875968992 + x = -0.201773877 + 0.003875968992

Combine like terms: -0.003875968992 + 0.003875968992 = 0.000000000000
0.000000000000 + x = -0.201773877 + 0.003875968992
x = -0.201773877 + 0.003875968992

Combine like terms: -0.201773877 + 0.003875968992 = -0.197897908008
x = -0.197897908008

Simplifying
x = -0.197897908008

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.205649845992, -0.197897908008}
Solution
x = {0.205649845992, -0.197897908008}