y(0)=-3x^2+19x+40

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Solution for y(0)=-3x^2+19x+40 equation: 


Simplifying
y(0) = -3x2 + 19x + 40

Reorder the terms for easier multiplication:
0y = -3x2 + 19x + 40

Anything times zero is zero.
0y = -3x2 + 19x + 40

Reorder the terms:
0 = 40 + 19x + -3x2

Solving
0 = 40 + 19x + -3x2

Solving for variable 'x'.

Combine like terms: 0 + -40 = -40
-40 + -19x + 3x2 = 40 + 19x + -3x2 + -40 + -19x + 3x2

Reorder the terms:
-40 + -19x + 3x2 = 40 + -40 + 19x + -19x + -3x2 + 3x2

Combine like terms: 40 + -40 = 0
-40 + -19x + 3x2 = 0 + 19x + -19x + -3x2 + 3x2
-40 + -19x + 3x2 = 19x + -19x + -3x2 + 3x2

Combine like terms: 19x + -19x = 0
-40 + -19x + 3x2 = 0 + -3x2 + 3x2
-40 + -19x + 3x2 = -3x2 + 3x2

Combine like terms: -3x2 + 3x2 = 0
-40 + -19x + 3x2 = 0

Factor a trinomial.
(-5 + -3x)(8 + -1x) = 0


Subproblem 1
Set the factor '(-5 + -3x)' equal to zero and attempt to solve:

Simplifying
-5 + -3x = 0

Solving
-5 + -3x = 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 + -3x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -3x = 0 + 5
-3x = 0 + 5

Combine like terms: 0 + 5 = 5
-3x = 5

Divide each side by '-3'.
x = -1.666666667

Simplifying
x = -1.666666667

Subproblem 2
Set the factor '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 0 + -8
-1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1x = -8

Divide each side by '-1'.
x = 8

Simplifying
x = 8
Solution
x = {-1.666666667, 8}

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