x(3x+7)=2(9+2x)

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Solution for x(3x+7)=2(9+2x) equation: 


Simplifying
x(3x + 7) = 2(9 + 2x)

Reorder the terms:
x(7 + 3x) = 2(9 + 2x)
(7 * x + 3x * x) = 2(9 + 2x)
(7x + 3x2) = 2(9 + 2x)
7x + 3x2 = (9 * 2 + 2x * 2)
7x + 3x2 = (18 + 4x)

Solving
7x + 3x2 = 18 + 4x

Solving for variable 'x'.

Reorder the terms:
-18 + 7x + -4x + 3x2 = 18 + 4x + -18 + -4x

Combine like terms: 7x + -4x = 3x
-18 + 3x + 3x2 = 18 + 4x + -18 + -4x

Reorder the terms:
-18 + 3x + 3x2 = 18 + -18 + 4x + -4x

Combine like terms: 18 + -18 = 0
-18 + 3x + 3x2 = 0 + 4x + -4x
-18 + 3x + 3x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
-18 + 3x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-6 + x + x2) = 0

Factor a trinomial.
3((-3 + -1x)(2 + -1x)) = 0

Ignore the factor 3.

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 '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-3, 2}

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