3x(x-1)=x^2+20

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Solution for 3x(x-1)=x^2+20 equation: 


Simplifying
3x(x + -1) = x2 + 20

Reorder the terms:
3x(-1 + x) = x2 + 20
(-1 * 3x + x * 3x) = x2 + 20
(-3x + 3x2) = x2 + 20

Reorder the terms:
-3x + 3x2 = 20 + x2

Solving
-3x + 3x2 = 20 + x2

Solving for variable 'x'.

Reorder the terms:
-20 + -3x + 3x2 + -1x2 = 20 + x2 + -20 + -1x2

Combine like terms: 3x2 + -1x2 = 2x2
-20 + -3x + 2x2 = 20 + x2 + -20 + -1x2

Reorder the terms:
-20 + -3x + 2x2 = 20 + -20 + x2 + -1x2

Combine like terms: 20 + -20 = 0
-20 + -3x + 2x2 = 0 + x2 + -1x2
-20 + -3x + 2x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-20 + -3x + 2x2 = 0

Factor a trinomial.
(-5 + -2x)(4 + -1x) = 0


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

Simplifying
-5 + -2x = 0

Solving
-5 + -2x = 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 + -2x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -2x = 0 + 5
-2x = 0 + 5

Combine like terms: 0 + 5 = 5
-2x = 5

Divide each side by '-2'.
x = -2.5

Simplifying
x = -2.5

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 = {-2.5, 4}

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