0=40-2x-3x^2

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Solution for 0=40-2x-3x^2 equation: 


Simplifying
0 = 40 + -2x + -3x2

Solving
0 = 40 + -2x + -3x2

Solving for variable 'x'.

Combine like terms: 0 + -40 = -40
-40 + 2x + 3x2 = 40 + -2x + -3x2 + -40 + 2x + 3x2

Reorder the terms:
-40 + 2x + 3x2 = 40 + -40 + -2x + 2x + -3x2 + 3x2

Combine like terms: 40 + -40 = 0
-40 + 2x + 3x2 = 0 + -2x + 2x + -3x2 + 3x2
-40 + 2x + 3x2 = -2x + 2x + -3x2 + 3x2

Combine like terms: -2x + 2x = 0
-40 + 2x + 3x2 = 0 + -3x2 + 3x2
-40 + 2x + 3x2 = -3x2 + 3x2

Combine like terms: -3x2 + 3x2 = 0
-40 + 2x + 3x2 = 0

Factor a trinomial.
(-4 + -1x)(10 + -3x) = 0


Subproblem 1
Set the factor '(-4 + -1x)' equal to zero and attempt to solve:

Simplifying
-4 + -1x = 0

Solving
-4 + -1x = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1x = 0 + 4
-1x = 0 + 4

Combine like terms: 0 + 4 = 4
-1x = 4

Divide each side by '-1'.
x = -4

Simplifying
x = -4

Subproblem 2
Set the factor '(10 + -3x)' equal to zero and attempt to solve:

Simplifying
10 + -3x = 0

Solving
10 + -3x = 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 + -3x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -3x = 0 + -10
-3x = 0 + -10

Combine like terms: 0 + -10 = -10
-3x = -10

Divide each side by '-3'.
x = 3.333333333

Simplifying
x = 3.333333333
Solution
x = {-4, 3.333333333}

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