2x^2+9x=3x^2-10

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Solution for 2x^2+9x=3x^2-10 equation: 


Simplifying
2x2 + 9x = 3x2 + -10

Reorder the terms:
9x + 2x2 = 3x2 + -10

Reorder the terms:
9x + 2x2 = -10 + 3x2

Solving
9x + 2x2 = -10 + 3x2

Solving for variable 'x'.

Reorder the terms:
10 + 9x + 2x2 + -3x2 = -10 + 3x2 + 10 + -3x2

Combine like terms: 2x2 + -3x2 = -1x2
10 + 9x + -1x2 = -10 + 3x2 + 10 + -3x2

Reorder the terms:
10 + 9x + -1x2 = -10 + 10 + 3x2 + -3x2

Combine like terms: -10 + 10 = 0
10 + 9x + -1x2 = 0 + 3x2 + -3x2
10 + 9x + -1x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
10 + 9x + -1x2 = 0

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


Subproblem 1
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

Subproblem 2
Set the factor '(1 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

Solving
1 + x = 0

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

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

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

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

Simplifying
x = -1
Solution
x = {10, -1}

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