x(9+17)=4x^2-12x+42

Solution for x(9+17)=4x^2-12x+42 equation:

Simplifying
x(9 + 17) = 4x2 + -12x + 42

Combine like terms: 9 + 17 = 26
x(26) = 4x2 + -12x + 42

Reorder the terms for easier multiplication:
26x = 4x2 + -12x + 42

Reorder the terms:
26x = 42 + -12x + 4x2

Solving
26x = 42 + -12x + 4x2

Solving for variable 'x'.

Reorder the terms:
-42 + 26x + 12x + -4x2 = 42 + -12x + 4x2 + -42 + 12x + -4x2

Combine like terms: 26x + 12x = 38x
-42 + 38x + -4x2 = 42 + -12x + 4x2 + -42 + 12x + -4x2

Reorder the terms:
-42 + 38x + -4x2 = 42 + -42 + -12x + 12x + 4x2 + -4x2

Combine like terms: 42 + -42 = 0
-42 + 38x + -4x2 = 0 + -12x + 12x + 4x2 + -4x2
-42 + 38x + -4x2 = -12x + 12x + 4x2 + -4x2

Combine like terms: -12x + 12x = 0
-42 + 38x + -4x2 = 0 + 4x2 + -4x2
-42 + 38x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-42 + 38x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-21 + 19x + -2x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-21 + 19x + -2x2)' equal to zero and attempt to solve:

Simplifying
-21 + 19x + -2x2 = 0

Solving
-21 + 19x + -2x2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
10.5 + -9.5x + x2 = 0

Move the constant term to the right:

Add '-10.5' to each side of the equation.
10.5 + -9.5x + -10.5 + x2 = 0 + -10.5

Reorder the terms:
10.5 + -10.5 + -9.5x + x2 = 0 + -10.5

Combine like terms: 10.5 + -10.5 = 0.0
0.0 + -9.5x + x2 = 0 + -10.5
-9.5x + x2 = 0 + -10.5

Combine like terms: 0 + -10.5 = -10.5
-9.5x + x2 = -10.5

The x term is -9.5x.  Take half its coefficient (-4.75).
Square it (22.5625) and add it to both sides.

Add '22.5625' to each side of the equation.
-9.5x + 22.5625 + x2 = -10.5 + 22.5625

Reorder the terms:
22.5625 + -9.5x + x2 = -10.5 + 22.5625

Combine like terms: -10.5 + 22.5625 = 12.0625
22.5625 + -9.5x + x2 = 12.0625

Factor a perfect square on the left side:
(x + -4.75)(x + -4.75) = 12.0625

Calculate the square root of the right side: 3.473110997

Break this problem into two subproblems by setting 
(x + -4.75) equal to 3.473110997 and -3.473110997.

Subproblem 1
x + -4.75 = 3.473110997

Simplifying
x + -4.75 = 3.473110997

Reorder the terms:
-4.75 + x = 3.473110997

Solving
-4.75 + x = 3.473110997

Solving for variable 'x'.

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

Add '4.75' to each side of the equation.
-4.75 + 4.75 + x = 3.473110997 + 4.75

Combine like terms: -4.75 + 4.75 = 0.00
0.00 + x = 3.473110997 + 4.75
x = 3.473110997 + 4.75

Combine like terms: 3.473110997 + 4.75 = 8.223110997
x = 8.223110997

Simplifying
x = 8.223110997

Subproblem 2
x + -4.75 = -3.473110997

Simplifying
x + -4.75 = -3.473110997

Reorder the terms:
-4.75 + x = -3.473110997

Solving
-4.75 + x = -3.473110997

Solving for variable 'x'.

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

Add '4.75' to each side of the equation.
-4.75 + 4.75 + x = -3.473110997 + 4.75

Combine like terms: -4.75 + 4.75 = 0.00
0.00 + x = -3.473110997 + 4.75
x = -3.473110997 + 4.75

Combine like terms: -3.473110997 + 4.75 = 1.276889003
x = 1.276889003

Simplifying
x = 1.276889003

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.223110997, 1.276889003}
Solution
x = {8.223110997, 1.276889003}