3x^2+21x+27=2x^2+37x-33

Solution for 3x^2+21x+27=2x^2+37x-33 equation:

Simplifying
3x2 + 21x + 27 = 2x2 + 37x + -33

Reorder the terms:
27 + 21x + 3x2 = 2x2 + 37x + -33

Reorder the terms:
27 + 21x + 3x2 = -33 + 37x + 2x2

Solving
27 + 21x + 3x2 = -33 + 37x + 2x2

Solving for variable 'x'.

Reorder the terms:
27 + 33 + 21x + -37x + 3x2 + -2x2 = -33 + 37x + 2x2 + 33 + -37x + -2x2

Combine like terms: 27 + 33 = 60
60 + 21x + -37x + 3x2 + -2x2 = -33 + 37x + 2x2 + 33 + -37x + -2x2

Combine like terms: 21x + -37x = -16x
60 + -16x + 3x2 + -2x2 = -33 + 37x + 2x2 + 33 + -37x + -2x2

Combine like terms: 3x2 + -2x2 = 1x2
60 + -16x + 1x2 = -33 + 37x + 2x2 + 33 + -37x + -2x2

Reorder the terms:
60 + -16x + 1x2 = -33 + 33 + 37x + -37x + 2x2 + -2x2

Combine like terms: -33 + 33 = 0
60 + -16x + 1x2 = 0 + 37x + -37x + 2x2 + -2x2
60 + -16x + 1x2 = 37x + -37x + 2x2 + -2x2

Combine like terms: 37x + -37x = 0
60 + -16x + 1x2 = 0 + 2x2 + -2x2
60 + -16x + 1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
60 + -16x + 1x2 = 0

Factor a trinomial.
(6 + -1x)(10 + -1x) = 0

Subproblem 1
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Subproblem 2
Set the factor '(10 + -1x)' equal to zero and attempt to solve:

Simplifying
10 + -1x = 0

Solving
10 + -1x = 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 + -1x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1x = 0 + -10
-1x = 0 + -10

Combine like terms: 0 + -10 = -10
-1x = -10

Divide each side by '-1'.
x = 10

Simplifying
x = 10
Solution
x = {6, 10}