5x^2=x^2+16x+20

Solution for 5x^2=x^2+16x+20 equation:

Simplifying
5x2 = x2 + 16x + 20

Reorder the terms:
5x2 = 20 + 16x + x2

Solving
5x2 = 20 + 16x + x2

Solving for variable 'x'.

Reorder the terms:
-20 + -16x + 5x2 + -1x2 = 20 + 16x + x2 + -20 + -16x + -1x2

Combine like terms: 5x2 + -1x2 = 4x2
-20 + -16x + 4x2 = 20 + 16x + x2 + -20 + -16x + -1x2

Reorder the terms:
-20 + -16x + 4x2 = 20 + -20 + 16x + -16x + x2 + -1x2

Combine like terms: 20 + -20 = 0
-20 + -16x + 4x2 = 0 + 16x + -16x + x2 + -1x2
-20 + -16x + 4x2 = 16x + -16x + x2 + -1x2

Combine like terms: 16x + -16x = 0
-20 + -16x + 4x2 = 0 + x2 + -1x2
-20 + -16x + 4x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-20 + -16x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-5 + -4x + x2) = 0

Factor a trinomial.
4((-1 + -1x)(5 + -1x)) = 0

Ignore the factor 4.
Subproblem 1
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
Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {-1, 5}