170x-150x+300=16x^2+32x

Solution for 170x-150x+300=16x^2+32x equation:

Simplifying
170x + -150x + 300 = 16x2 + 32x

Reorder the terms:
300 + 170x + -150x = 16x2 + 32x

Combine like terms: 170x + -150x = 20x
300 + 20x = 16x2 + 32x

Reorder the terms:
300 + 20x = 32x + 16x2

Solving
300 + 20x = 32x + 16x2

Solving for variable 'x'.

Combine like terms: 20x + -32x = -12x
300 + -12x + -16x2 = 32x + 16x2 + -32x + -16x2

Reorder the terms:
300 + -12x + -16x2 = 32x + -32x + 16x2 + -16x2

Combine like terms: 32x + -32x = 0
300 + -12x + -16x2 = 0 + 16x2 + -16x2
300 + -12x + -16x2 = 16x2 + -16x2

Combine like terms: 16x2 + -16x2 = 0
300 + -12x + -16x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(75 + -3x + -4x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(75 + -3x + -4x2)' equal to zero and attempt to solve:

Simplifying
75 + -3x + -4x2 = 0

Solving
75 + -3x + -4x2 = 0

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
-18.75 + 0.75x + x2 = 0

Move the constant term to the right:

Add '18.75' to each side of the equation.
-18.75 + 0.75x + 18.75 + x2 = 0 + 18.75

Reorder the terms:
-18.75 + 18.75 + 0.75x + x2 = 0 + 18.75

Combine like terms: -18.75 + 18.75 = 0.00
0.00 + 0.75x + x2 = 0 + 18.75
0.75x + x2 = 0 + 18.75

Combine like terms: 0 + 18.75 = 18.75
0.75x + x2 = 18.75

The x term is 0.75x.  Take half its coefficient (0.375).
Square it (0.140625) and add it to both sides.

Add '0.140625' to each side of the equation.
0.75x + 0.140625 + x2 = 18.75 + 0.140625

Reorder the terms:
0.140625 + 0.75x + x2 = 18.75 + 0.140625

Combine like terms: 18.75 + 0.140625 = 18.890625
0.140625 + 0.75x + x2 = 18.890625

Factor a perfect square on the left side:
(x + 0.375)(x + 0.375) = 18.890625

Calculate the square root of the right side: 4.346334663

Break this problem into two subproblems by setting 
(x + 0.375) equal to 4.346334663 and -4.346334663.

Subproblem 1
x + 0.375 = 4.346334663

Simplifying
x + 0.375 = 4.346334663

Reorder the terms:
0.375 + x = 4.346334663

Solving
0.375 + x = 4.346334663

Solving for variable 'x'.

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

Add '-0.375' to each side of the equation.
0.375 + -0.375 + x = 4.346334663 + -0.375

Combine like terms: 0.375 + -0.375 = 0.000
0.000 + x = 4.346334663 + -0.375
x = 4.346334663 + -0.375

Combine like terms: 4.346334663 + -0.375 = 3.971334663
x = 3.971334663

Simplifying
x = 3.971334663

Subproblem 2
x + 0.375 = -4.346334663

Simplifying
x + 0.375 = -4.346334663

Reorder the terms:
0.375 + x = -4.346334663

Solving
0.375 + x = -4.346334663

Solving for variable 'x'.

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

Add '-0.375' to each side of the equation.
0.375 + -0.375 + x = -4.346334663 + -0.375

Combine like terms: 0.375 + -0.375 = 0.000
0.000 + x = -4.346334663 + -0.375
x = -4.346334663 + -0.375

Combine like terms: -4.346334663 + -0.375 = -4.721334663
x = -4.721334663

Simplifying
x = -4.721334663

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.971334663, -4.721334663}
Solution
x = {3.971334663, -4.721334663}