3x^2+7x=20+3x

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Solution for 3x^2+7x=20+3x equation: 


Simplifying
3x2 + 7x = 20 + 3x

Reorder the terms:
7x + 3x2 = 20 + 3x

Solving
7x + 3x2 = 20 + 3x

Solving for variable 'x'.

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

Combine like terms: 7x + -3x = 4x
-20 + 4x + 3x2 = 20 + 3x + -20 + -3x

Reorder the terms:
-20 + 4x + 3x2 = 20 + -20 + 3x + -3x

Combine like terms: 20 + -20 = 0
-20 + 4x + 3x2 = 0 + 3x + -3x
-20 + 4x + 3x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
-20 + 4x + 3x2 = 0

Factor a trinomial.
(-10 + -3x)(2 + -1x) = 0


Subproblem 1
Set the factor '(-10 + -3x)' equal to zero and attempt to solve:

Simplifying
-10 + -3x = 0

Solving
-10 + -3x = 0

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

Add '10' to each side of the equation.
-10 + 10 + -3x = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -3x = 0 + 10
-3x = 0 + 10

Combine like terms: 0 + 10 = 10
-3x = 10

Divide each side by '-3'.
x = -3.333333333

Simplifying
x = -3.333333333

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 = {-3.333333333, 2}

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