546=(45-6*8+2x)(367-43x)

Solution for 546=(45-6*8+2x)(367-43x) equation:

Simplifying
546 = (45 + -6 * 8 + 2x)(367 + -43x)

Multiply -6 * 8
546 = (45 + -48 + 2x)(367 + -43x)

Combine like terms: 45 + -48 = -3
546 = (-3 + 2x)(367 + -43x)

Multiply (-3 + 2x) * (367 + -43x)
546 = (-3(367 + -43x) + 2x * (367 + -43x))
546 = ((367 * -3 + -43x * -3) + 2x * (367 + -43x))
546 = ((-1101 + 129x) + 2x * (367 + -43x))
546 = (-1101 + 129x + (367 * 2x + -43x * 2x))
546 = (-1101 + 129x + (734x + -86x2))

Combine like terms: 129x + 734x = 863x
546 = (-1101 + 863x + -86x2)

Solving
546 = -1101 + 863x + -86x2

Solving for variable 'x'.

Combine like terms: 546 + 1101 = 1647
1647 + -863x + 86x2 = -1101 + 863x + -86x2 + 1101 + -863x + 86x2

Reorder the terms:
1647 + -863x + 86x2 = -1101 + 1101 + 863x + -863x + -86x2 + 86x2

Combine like terms: -1101 + 1101 = 0
1647 + -863x + 86x2 = 0 + 863x + -863x + -86x2 + 86x2
1647 + -863x + 86x2 = 863x + -863x + -86x2 + 86x2

Combine like terms: 863x + -863x = 0
1647 + -863x + 86x2 = 0 + -86x2 + 86x2
1647 + -863x + 86x2 = -86x2 + 86x2

Combine like terms: -86x2 + 86x2 = 0
1647 + -863x + 86x2 = 0

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

Divide each side by '86'.
19.15116279 + -10.03488372x + x2 = 0

Move the constant term to the right:

Add '-19.15116279' to each side of the equation.
19.15116279 + -10.03488372x + -19.15116279 + x2 = 0 + -19.15116279

Reorder the terms:
19.15116279 + -19.15116279 + -10.03488372x + x2 = 0 + -19.15116279

Combine like terms: 19.15116279 + -19.15116279 = 0.00000000
0.00000000 + -10.03488372x + x2 = 0 + -19.15116279
-10.03488372x + x2 = 0 + -19.15116279

Combine like terms: 0 + -19.15116279 = -19.15116279
-10.03488372x + x2 = -19.15116279

The x term is -10.03488372x.  Take half its coefficient (-5.01744186).
Square it (25.17472282) and add it to both sides.

Add '25.17472282' to each side of the equation.
-10.03488372x + 25.17472282 + x2 = -19.15116279 + 25.17472282

Reorder the terms:
25.17472282 + -10.03488372x + x2 = -19.15116279 + 25.17472282

Combine like terms: -19.15116279 + 25.17472282 = 6.02356003
25.17472282 + -10.03488372x + x2 = 6.02356003

Factor a perfect square on the left side:
(x + -5.01744186)(x + -5.01744186) = 6.02356003

Calculate the square root of the right side: 2.454294202

Break this problem into two subproblems by setting 
(x + -5.01744186) equal to 2.454294202 and -2.454294202.

Subproblem 1
x + -5.01744186 = 2.454294202

Simplifying
x + -5.01744186 = 2.454294202

Reorder the terms:
-5.01744186 + x = 2.454294202

Solving
-5.01744186 + x = 2.454294202

Solving for variable 'x'.

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

Add '5.01744186' to each side of the equation.
-5.01744186 + 5.01744186 + x = 2.454294202 + 5.01744186

Combine like terms: -5.01744186 + 5.01744186 = 0.00000000
0.00000000 + x = 2.454294202 + 5.01744186
x = 2.454294202 + 5.01744186

Combine like terms: 2.454294202 + 5.01744186 = 7.471736062
x = 7.471736062

Simplifying
x = 7.471736062

Subproblem 2
x + -5.01744186 = -2.454294202

Simplifying
x + -5.01744186 = -2.454294202

Reorder the terms:
-5.01744186 + x = -2.454294202

Solving
-5.01744186 + x = -2.454294202

Solving for variable 'x'.

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

Add '5.01744186' to each side of the equation.
-5.01744186 + 5.01744186 + x = -2.454294202 + 5.01744186

Combine like terms: -5.01744186 + 5.01744186 = 0.00000000
0.00000000 + x = -2.454294202 + 5.01744186
x = -2.454294202 + 5.01744186

Combine like terms: -2.454294202 + 5.01744186 = 2.563147658
x = 2.563147658

Simplifying
x = 2.563147658

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.471736062, 2.563147658}