x(x+5)=3(x+21)

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Solution for x(x+5)=3(x+21) equation: 


Simplifying
x(x + 5) = 3(x + 21)

Reorder the terms:
x(5 + x) = 3(x + 21)
(5 * x + x * x) = 3(x + 21)
(5x + x2) = 3(x + 21)

Reorder the terms:
5x + x2 = 3(21 + x)
5x + x2 = (21 * 3 + x * 3)
5x + x2 = (63 + 3x)

Solving
5x + x2 = 63 + 3x

Solving for variable 'x'.

Reorder the terms:
-63 + 5x + -3x + x2 = 63 + 3x + -63 + -3x

Combine like terms: 5x + -3x = 2x
-63 + 2x + x2 = 63 + 3x + -63 + -3x

Reorder the terms:
-63 + 2x + x2 = 63 + -63 + 3x + -3x

Combine like terms: 63 + -63 = 0
-63 + 2x + x2 = 0 + 3x + -3x
-63 + 2x + x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
-63 + 2x + x2 = 0

Factor a trinomial.
(-9 + -1x)(7 + -1x) = 0


Subproblem 1
Set the factor '(-9 + -1x)' equal to zero and attempt to solve:

Simplifying
-9 + -1x = 0

Solving
-9 + -1x = 0

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

Add '9' to each side of the equation.
-9 + 9 + -1x = 0 + 9

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

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

Divide each side by '-1'.
x = -9

Simplifying
x = -9

Subproblem 2
Set the factor '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {-9, 7}

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