0=-6X^2+3X+9

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Solution for 0=-6X^2+3X+9 equation:


Simplifying
0 = -6X2 + 3X + 9

Reorder the terms:
0 = 9 + 3X + -6X2

Solving
0 = 9 + 3X + -6X2

Solving for variable 'X'.

Combine like terms: 0 + -9 = -9
-9 + -3X + 6X2 = 9 + 3X + -6X2 + -9 + -3X + 6X2

Reorder the terms:
-9 + -3X + 6X2 = 9 + -9 + 3X + -3X + -6X2 + 6X2

Combine like terms: 9 + -9 = 0
-9 + -3X + 6X2 = 0 + 3X + -3X + -6X2 + 6X2
-9 + -3X + 6X2 = 3X + -3X + -6X2 + 6X2

Combine like terms: 3X + -3X = 0
-9 + -3X + 6X2 = 0 + -6X2 + 6X2
-9 + -3X + 6X2 = -6X2 + 6X2

Combine like terms: -6X2 + 6X2 = 0
-9 + -3X + 6X2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-3 + -1X + 2X2) = 0

Factor a trinomial.
3((-1 + -1X)(3 + -2X)) = 0

Ignore the factor 3.

Subproblem 1

Set the factor '(-1 + -1X)' equal to zero and attempt to solve: Simplifying -1 + -1X = 0 Solving -1 + -1X = 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 + -1X = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1X = 0 + 1 -1X = 0 + 1 Combine like terms: 0 + 1 = 1 -1X = 1 Divide each side by '-1'. X = -1 Simplifying X = -1

Subproblem 2

Set the factor '(3 + -2X)' equal to zero and attempt to solve: Simplifying 3 + -2X = 0 Solving 3 + -2X = 0 Move all terms containing X to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -2X = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2X = 0 + -3 -2X = 0 + -3 Combine like terms: 0 + -3 = -3 -2X = -3 Divide each side by '-2'. X = 1.5 Simplifying X = 1.5

Solution

X = {-1, 1.5}

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