9x^2+38x+20=2x^2+3x-8

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Solution for 9x^2+38x+20=2x^2+3x-8 equation: 


Simplifying
9x2 + 38x + 20 = 2x2 + 3x + -8

Reorder the terms:
20 + 38x + 9x2 = 2x2 + 3x + -8

Reorder the terms:
20 + 38x + 9x2 = -8 + 3x + 2x2

Solving
20 + 38x + 9x2 = -8 + 3x + 2x2

Solving for variable 'x'.

Reorder the terms:
20 + 8 + 38x + -3x + 9x2 + -2x2 = -8 + 3x + 2x2 + 8 + -3x + -2x2

Combine like terms: 20 + 8 = 28
28 + 38x + -3x + 9x2 + -2x2 = -8 + 3x + 2x2 + 8 + -3x + -2x2

Combine like terms: 38x + -3x = 35x
28 + 35x + 9x2 + -2x2 = -8 + 3x + 2x2 + 8 + -3x + -2x2

Combine like terms: 9x2 + -2x2 = 7x2
28 + 35x + 7x2 = -8 + 3x + 2x2 + 8 + -3x + -2x2

Reorder the terms:
28 + 35x + 7x2 = -8 + 8 + 3x + -3x + 2x2 + -2x2

Combine like terms: -8 + 8 = 0
28 + 35x + 7x2 = 0 + 3x + -3x + 2x2 + -2x2
28 + 35x + 7x2 = 3x + -3x + 2x2 + -2x2

Combine like terms: 3x + -3x = 0
28 + 35x + 7x2 = 0 + 2x2 + -2x2
28 + 35x + 7x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
28 + 35x + 7x2 = 0

Factor out the Greatest Common Factor (GCF), '7'.
7(4 + 5x + x2) = 0

Factor a trinomial.
7((4 + x)(1 + x)) = 0

Ignore the factor 7.

Subproblem 1
Set the factor '(4 + x)' equal to zero and attempt to solve:

Simplifying
4 + x = 0

Solving
4 + x = 0

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

Add '-4' to each side of the equation.
4 + -4 + x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + x = 0 + -4
x = 0 + -4

Combine like terms: 0 + -4 = -4
x = -4

Simplifying
x = -4

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

Simplifying
1 + x = 0

Solving
1 + x = 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 + x = 0 + -1

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

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

Simplifying
x = -1
Solution
x = {-4, -1}

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