-3x^2+5x+21=-2x^2+3x+13

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Solution for -3x^2+5x+21=-2x^2+3x+13 equation: 


Simplifying
-3x2 + 5x + 21 = -2x2 + 3x + 13

Reorder the terms:
21 + 5x + -3x2 = -2x2 + 3x + 13

Reorder the terms:
21 + 5x + -3x2 = 13 + 3x + -2x2

Solving
21 + 5x + -3x2 = 13 + 3x + -2x2

Solving for variable 'x'.

Reorder the terms:
21 + -13 + 5x + -3x + -3x2 + 2x2 = 13 + 3x + -2x2 + -13 + -3x + 2x2

Combine like terms: 21 + -13 = 8
8 + 5x + -3x + -3x2 + 2x2 = 13 + 3x + -2x2 + -13 + -3x + 2x2

Combine like terms: 5x + -3x = 2x
8 + 2x + -3x2 + 2x2 = 13 + 3x + -2x2 + -13 + -3x + 2x2

Combine like terms: -3x2 + 2x2 = -1x2
8 + 2x + -1x2 = 13 + 3x + -2x2 + -13 + -3x + 2x2

Reorder the terms:
8 + 2x + -1x2 = 13 + -13 + 3x + -3x + -2x2 + 2x2

Combine like terms: 13 + -13 = 0
8 + 2x + -1x2 = 0 + 3x + -3x + -2x2 + 2x2
8 + 2x + -1x2 = 3x + -3x + -2x2 + 2x2

Combine like terms: 3x + -3x = 0
8 + 2x + -1x2 = 0 + -2x2 + 2x2
8 + 2x + -1x2 = -2x2 + 2x2

Combine like terms: -2x2 + 2x2 = 0
8 + 2x + -1x2 = 0

Factor a trinomial.
(4 + -1x)(2 + x) = 0


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

Simplifying
4 + -1x = 0

Solving
4 + -1x = 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 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4

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

Simplifying
2 + x = 0

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

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

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

Simplifying
x = -2
Solution
x = {4, -2}

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