5x+7=2x+3x(x+9)-20

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Solution for 5x+7=2x+3x(x+9)-20 equation: 


Simplifying
5x + 7 = 2x + 3x(x + 9) + -20

Reorder the terms:
7 + 5x = 2x + 3x(x + 9) + -20

Reorder the terms:
7 + 5x = 2x + 3x(9 + x) + -20
7 + 5x = 2x + (9 * 3x + x * 3x) + -20
7 + 5x = 2x + (27x + 3x2) + -20

Reorder the terms:
7 + 5x = -20 + 2x + 27x + 3x2

Combine like terms: 2x + 27x = 29x
7 + 5x = -20 + 29x + 3x2

Solving
7 + 5x = -20 + 29x + 3x2

Solving for variable 'x'.

Reorder the terms:
7 + 20 + 5x + -29x + -3x2 = -20 + 29x + 3x2 + 20 + -29x + -3x2

Combine like terms: 7 + 20 = 27
27 + 5x + -29x + -3x2 = -20 + 29x + 3x2 + 20 + -29x + -3x2

Combine like terms: 5x + -29x = -24x
27 + -24x + -3x2 = -20 + 29x + 3x2 + 20 + -29x + -3x2

Reorder the terms:
27 + -24x + -3x2 = -20 + 20 + 29x + -29x + 3x2 + -3x2

Combine like terms: -20 + 20 = 0
27 + -24x + -3x2 = 0 + 29x + -29x + 3x2 + -3x2
27 + -24x + -3x2 = 29x + -29x + 3x2 + -3x2

Combine like terms: 29x + -29x = 0
27 + -24x + -3x2 = 0 + 3x2 + -3x2
27 + -24x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
27 + -24x + -3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(9 + -8x + -1x2) = 0

Factor a trinomial.
3((1 + -1x)(9 + x)) = 0

Ignore the factor 3.

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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

Simplifying
x = 1

Subproblem 2
Set the factor '(9 + x)' equal to zero and attempt to solve:

Simplifying
9 + x = 0

Solving
9 + x = 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 + x = 0 + -9

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

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

Simplifying
x = -9
Solution
x = {1, -9}

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