27x+54=x^2+16x+64

Solution for 27x+54=x^2+16x+64 equation:

Simplifying
27x + 54 = x2 + 16x + 64

Reorder the terms:
54 + 27x = x2 + 16x + 64

Reorder the terms:
54 + 27x = 64 + 16x + x2

Solving
54 + 27x = 64 + 16x + x2

Solving for variable 'x'.

Reorder the terms:
54 + -64 + 27x + -16x + -1x2 = 64 + 16x + x2 + -64 + -16x + -1x2

Combine like terms: 54 + -64 = -10
-10 + 27x + -16x + -1x2 = 64 + 16x + x2 + -64 + -16x + -1x2

Combine like terms: 27x + -16x = 11x
-10 + 11x + -1x2 = 64 + 16x + x2 + -64 + -16x + -1x2

Reorder the terms:
-10 + 11x + -1x2 = 64 + -64 + 16x + -16x + x2 + -1x2

Combine like terms: 64 + -64 = 0
-10 + 11x + -1x2 = 0 + 16x + -16x + x2 + -1x2
-10 + 11x + -1x2 = 16x + -16x + x2 + -1x2

Combine like terms: 16x + -16x = 0
-10 + 11x + -1x2 = 0 + x2 + -1x2
-10 + 11x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-10 + 11x + -1x2 = 0

Factor a trinomial.
(-10 + x)(1 + -1x) = 0

Subproblem 1
Set the factor '(-10 + x)' equal to zero and attempt to solve:

Simplifying
-10 + x = 0

Solving
-10 + x = 0

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

Add '10' to each side of the equation.
-10 + 10 + x = 0 + 10

Combine like terms: -10 + 10 = 0
0 + x = 0 + 10
x = 0 + 10

Combine like terms: 0 + 10 = 10
x = 10

Simplifying
x = 10
Subproblem 2
Set the factor '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

Simplifying
x = 1
Solution
x = {10, 1}