13x^2+21x=-5x^2+22

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Solution for 13x^2+21x=-5x^2+22 equation: 


Simplifying
13x2 + 21x = -5x2 + 22

Reorder the terms:
21x + 13x2 = -5x2 + 22

Reorder the terms:
21x + 13x2 = 22 + -5x2

Solving
21x + 13x2 = 22 + -5x2

Solving for variable 'x'.

Reorder the terms:
-22 + 21x + 13x2 + 5x2 = 22 + -5x2 + -22 + 5x2

Combine like terms: 13x2 + 5x2 = 18x2
-22 + 21x + 18x2 = 22 + -5x2 + -22 + 5x2

Reorder the terms:
-22 + 21x + 18x2 = 22 + -22 + -5x2 + 5x2

Combine like terms: 22 + -22 = 0
-22 + 21x + 18x2 = 0 + -5x2 + 5x2
-22 + 21x + 18x2 = -5x2 + 5x2

Combine like terms: -5x2 + 5x2 = 0
-22 + 21x + 18x2 = 0

Factor a trinomial.
(-11 + -6x)(2 + -3x) = 0


Subproblem 1
Set the factor '(-11 + -6x)' equal to zero and attempt to solve:

Simplifying
-11 + -6x = 0

Solving
-11 + -6x = 0

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

Add '11' to each side of the equation.
-11 + 11 + -6x = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -6x = 0 + 11
-6x = 0 + 11

Combine like terms: 0 + 11 = 11
-6x = 11

Divide each side by '-6'.
x = -1.833333333

Simplifying
x = -1.833333333

Subproblem 2
Set the factor '(2 + -3x)' equal to zero and attempt to solve:

Simplifying
2 + -3x = 0

Solving
2 + -3x = 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 + -3x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3x = 0 + -2
-3x = 0 + -2

Combine like terms: 0 + -2 = -2
-3x = -2

Divide each side by '-3'.
x = 0.6666666667

Simplifying
x = 0.6666666667
Solution
x = {-1.833333333, 0.6666666667}

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