# -9x=2x^2-5

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## Solution for -9x=2x^2-5 equation:

Simplifying
-9x = 2x2 + -5

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

Solving
-9x = -5 + 2x2

Solving for variable 'x'.

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

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

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

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

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

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

Simplifying
5 + x = 0

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

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

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

Simplifying
x = -5Solutionx = {0.5, -5}`