62x-2x^2=38x+54

Solution for 62x-2x^2=38x+54 equation:

Simplifying
62x + -2x2 = 38x + 54

Reorder the terms:
62x + -2x2 = 54 + 38x

Solving
62x + -2x2 = 54 + 38x

Solving for variable 'x'.

Reorder the terms:
-54 + 62x + -38x + -2x2 = 54 + 38x + -54 + -38x

Combine like terms: 62x + -38x = 24x
-54 + 24x + -2x2 = 54 + 38x + -54 + -38x

Reorder the terms:
-54 + 24x + -2x2 = 54 + -54 + 38x + -38x

Combine like terms: 54 + -54 = 0
-54 + 24x + -2x2 = 0 + 38x + -38x
-54 + 24x + -2x2 = 38x + -38x

Combine like terms: 38x + -38x = 0
-54 + 24x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-27 + 12x + -1x2) = 0

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

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

Simplifying
-9 + x = 0

Solving
-9 + x = 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 + x = 0 + 9

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

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

Simplifying
x = 9
Subproblem 2
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
Solution
x = {9, 3}