2x^2-20=x^2+9x+16

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Solution for 2x^2-20=x^2+9x+16 equation: 


Simplifying
2x2 + -20 = x2 + 9x + 16

Reorder the terms:
-20 + 2x2 = x2 + 9x + 16

Reorder the terms:
-20 + 2x2 = 16 + 9x + x2

Solving
-20 + 2x2 = 16 + 9x + x2

Solving for variable 'x'.

Reorder the terms:
-20 + -16 + -9x + 2x2 + -1x2 = 16 + 9x + x2 + -16 + -9x + -1x2

Combine like terms: -20 + -16 = -36
-36 + -9x + 2x2 + -1x2 = 16 + 9x + x2 + -16 + -9x + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
-36 + -9x + 1x2 = 16 + 9x + x2 + -16 + -9x + -1x2

Reorder the terms:
-36 + -9x + 1x2 = 16 + -16 + 9x + -9x + x2 + -1x2

Combine like terms: 16 + -16 = 0
-36 + -9x + 1x2 = 0 + 9x + -9x + x2 + -1x2
-36 + -9x + 1x2 = 9x + -9x + x2 + -1x2

Combine like terms: 9x + -9x = 0
-36 + -9x + 1x2 = 0 + x2 + -1x2
-36 + -9x + 1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-36 + -9x + 1x2 = 0

Factor a trinomial.
(-3 + -1x)(12 + -1x) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(12 + -1x)' equal to zero and attempt to solve:

Simplifying
12 + -1x = 0

Solving
12 + -1x = 0

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

Add '-12' to each side of the equation.
12 + -12 + -1x = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1x = 0 + -12
-1x = 0 + -12

Combine like terms: 0 + -12 = -12
-1x = -12

Divide each side by '-1'.
x = 12

Simplifying
x = 12
Solution
x = {-3, 12}

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