5x^2-20x=x^2-16

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


Simplifying
5x2 + -20x = x2 + -16

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

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

Solving
-20x + 5x2 = -16 + x2

Solving for variable 'x'.

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

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

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

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

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

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

Factor a trinomial.
4((1 + -1x)(4 + -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 '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {1, 4}

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