0=2x^2+9x+10

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Solution for 0=2x^2+9x+10 equation: 


Simplifying
0 = 2x2 + 9x + 10

Reorder the terms:
0 = 10 + 9x + 2x2

Solving
0 = 10 + 9x + 2x2

Solving for variable 'x'.

Combine like terms: 0 + -10 = -10
-10 + -9x + -2x2 = 10 + 9x + 2x2 + -10 + -9x + -2x2

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

Combine like terms: 10 + -10 = 0
-10 + -9x + -2x2 = 0 + 9x + -9x + 2x2 + -2x2
-10 + -9x + -2x2 = 9x + -9x + 2x2 + -2x2

Combine like terms: 9x + -9x = 0
-10 + -9x + -2x2 = 0 + 2x2 + -2x2
-10 + -9x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-10 + -9x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(10 + 9x + 2x2) = 0

Factor a trinomial.
-1((5 + 2x)(2 + x)) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(5 + 2x)' equal to zero and attempt to solve:

Simplifying
5 + 2x = 0

Solving
5 + 2x = 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 + 2x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 2x = 0 + -5
2x = 0 + -5

Combine like terms: 0 + -5 = -5
2x = -5

Divide each side by '2'.
x = -2.5

Simplifying
x = -2.5

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 = {-2.5, -2}

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