28x+54=52x-2x^2

Solution for 28x+54=52x-2x^2 equation:

Simplifying
28x + 54 = 52x + -2x2

Reorder the terms:
54 + 28x = 52x + -2x2

Solving
54 + 28x = 52x + -2x2

Solving for variable 'x'.

Combine like terms: 28x + -52x = -24x
54 + -24x + 2x2 = 52x + -2x2 + -52x + 2x2

Reorder the terms:
54 + -24x + 2x2 = 52x + -52x + -2x2 + 2x2

Combine like terms: 52x + -52x = 0
54 + -24x + 2x2 = 0 + -2x2 + 2x2
54 + -24x + 2x2 = -2x2 + 2x2

Combine like terms: -2x2 + 2x2 = 0
54 + -24x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(27 + -12x + x2) = 0

Factor a trinomial.
2((3 + -1x)(9 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Subproblem 2
Set the factor '(9 + -1x)' equal to zero and attempt to solve:

Simplifying
9 + -1x = 0

Solving
9 + -1x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1x = 0 + -9
-1x = 0 + -9

Combine like terms: 0 + -9 = -9
-1x = -9

Divide each side by '-1'.
x = 9

Simplifying
x = 9
Solution
x = {3, 9}