7=2x^2+5x+9

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Solution for 7=2x^2+5x+9 equation: 


Simplifying
7 = 2x2 + 5x + 9

Reorder the terms:
7 = 9 + 5x + 2x2

Solving
7 = 9 + 5x + 2x2

Solving for variable 'x'.

Combine like terms: 7 + -9 = -2
-2 + -5x + -2x2 = 9 + 5x + 2x2 + -9 + -5x + -2x2

Reorder the terms:
-2 + -5x + -2x2 = 9 + -9 + 5x + -5x + 2x2 + -2x2

Combine like terms: 9 + -9 = 0
-2 + -5x + -2x2 = 0 + 5x + -5x + 2x2 + -2x2
-2 + -5x + -2x2 = 5x + -5x + 2x2 + -2x2

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

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

Factor out the Greatest Common Factor (GCF), '-1'.
-1(2 + 5x + 2x2) = 0

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

Ignore the factor -1.

Subproblem 1
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

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

Simplifying
1 + 2x = 0

Solving
1 + 2x = 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 + 2x = 0 + -1

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

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

Divide each side by '2'.
x = -0.5

Simplifying
x = -0.5
Solution
x = {-2, -0.5}

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