x(x+1)=3(x+16)

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Solution for x(x+1)=3(x+16) equation: 


Simplifying
x(x + 1) = 3(x + 16)

Reorder the terms:
x(1 + x) = 3(x + 16)
(1 * x + x * x) = 3(x + 16)
(1x + x2) = 3(x + 16)

Reorder the terms:
1x + x2 = 3(16 + x)
1x + x2 = (16 * 3 + x * 3)
1x + x2 = (48 + 3x)

Solving
1x + x2 = 48 + 3x

Solving for variable 'x'.

Reorder the terms:
-48 + 1x + -3x + x2 = 48 + 3x + -48 + -3x

Combine like terms: 1x + -3x = -2x
-48 + -2x + x2 = 48 + 3x + -48 + -3x

Reorder the terms:
-48 + -2x + x2 = 48 + -48 + 3x + -3x

Combine like terms: 48 + -48 = 0
-48 + -2x + x2 = 0 + 3x + -3x
-48 + -2x + x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
-48 + -2x + x2 = 0

Factor a trinomial.
(-6 + -1x)(8 + -1x) = 0


Subproblem 1
Set the factor '(-6 + -1x)' equal to zero and attempt to solve:

Simplifying
-6 + -1x = 0

Solving
-6 + -1x = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1x = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1x = 0 + 6
-1x = 0 + 6

Combine like terms: 0 + 6 = 6
-1x = 6

Divide each side by '-1'.
x = -6

Simplifying
x = -6

Subproblem 2
Set the factor '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 0 + -8
-1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1x = -8

Divide each side by '-1'.
x = 8

Simplifying
x = 8
Solution
x = {-6, 8}

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