3x^2+18x+21=x(x+5)

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Solution for 3x^2+18x+21=x(x+5) equation: 


Simplifying
3x2 + 18x + 21 = x(x + 5)

Reorder the terms:
21 + 18x + 3x2 = x(x + 5)

Reorder the terms:
21 + 18x + 3x2 = x(5 + x)
21 + 18x + 3x2 = (5 * x + x * x)
21 + 18x + 3x2 = (5x + x2)

Solving
21 + 18x + 3x2 = 5x + x2

Solving for variable 'x'.

Reorder the terms:
21 + 18x + -5x + 3x2 + -1x2 = 5x + x2 + -5x + -1x2

Combine like terms: 18x + -5x = 13x
21 + 13x + 3x2 + -1x2 = 5x + x2 + -5x + -1x2

Combine like terms: 3x2 + -1x2 = 2x2
21 + 13x + 2x2 = 5x + x2 + -5x + -1x2

Reorder the terms:
21 + 13x + 2x2 = 5x + -5x + x2 + -1x2

Combine like terms: 5x + -5x = 0
21 + 13x + 2x2 = 0 + x2 + -1x2
21 + 13x + 2x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
21 + 13x + 2x2 = 0

Factor a trinomial.
(7 + 2x)(3 + x) = 0


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

Simplifying
7 + 2x = 0

Solving
7 + 2x = 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 + 2x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 2x = 0 + -7
2x = 0 + -7

Combine like terms: 0 + -7 = -7
2x = -7

Divide each side by '2'.
x = -3.5

Simplifying
x = -3.5

Subproblem 2
Set the factor '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 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 + x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + x = 0 + -3
x = 0 + -3

Combine like terms: 0 + -3 = -3
x = -3

Simplifying
x = -3
Solution
x = {-3.5, -3}

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