2x^2-3x+30=3x^2-5x+15

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Solution for 2x^2-3x+30=3x^2-5x+15 equation: 


Simplifying
2x2 + -3x + 30 = 3x2 + -5x + 15

Reorder the terms:
30 + -3x + 2x2 = 3x2 + -5x + 15

Reorder the terms:
30 + -3x + 2x2 = 15 + -5x + 3x2

Solving
30 + -3x + 2x2 = 15 + -5x + 3x2

Solving for variable 'x'.

Reorder the terms:
30 + -15 + -3x + 5x + 2x2 + -3x2 = 15 + -5x + 3x2 + -15 + 5x + -3x2

Combine like terms: 30 + -15 = 15
15 + -3x + 5x + 2x2 + -3x2 = 15 + -5x + 3x2 + -15 + 5x + -3x2

Combine like terms: -3x + 5x = 2x
15 + 2x + 2x2 + -3x2 = 15 + -5x + 3x2 + -15 + 5x + -3x2

Combine like terms: 2x2 + -3x2 = -1x2
15 + 2x + -1x2 = 15 + -5x + 3x2 + -15 + 5x + -3x2

Reorder the terms:
15 + 2x + -1x2 = 15 + -15 + -5x + 5x + 3x2 + -3x2

Combine like terms: 15 + -15 = 0
15 + 2x + -1x2 = 0 + -5x + 5x + 3x2 + -3x2
15 + 2x + -1x2 = -5x + 5x + 3x2 + -3x2

Combine like terms: -5x + 5x = 0
15 + 2x + -1x2 = 0 + 3x2 + -3x2
15 + 2x + -1x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
15 + 2x + -1x2 = 0

Factor a trinomial.
(5 + -1x)(3 + x) = 0


Subproblem 1
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5

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

Simplifying
3 + x = 0

Solving
3 + x = 0

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

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

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

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

Simplifying
x = -3
Solution
x = {5, -3}

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