3*x^2=6*x+9

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Solution for 3*x^2=6*x+9 equation:


Simplifying
3x2 = 6x + 9

Reorder the terms:
3x2 = 9 + 6x

Solving
3x2 = 9 + 6x

Solving for variable 'x'.

Reorder the terms:
-9 + -6x + 3x2 = 9 + 6x + -9 + -6x

Reorder the terms:
-9 + -6x + 3x2 = 9 + -9 + 6x + -6x

Combine like terms: 9 + -9 = 0
-9 + -6x + 3x2 = 0 + 6x + -6x
-9 + -6x + 3x2 = 6x + -6x

Combine like terms: 6x + -6x = 0
-9 + -6x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-3 + -2x + x2) = 0

Factor a trinomial.
3((-1 + -1x)(3 + -1x)) = 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 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 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 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3

Solution

x = {-1, 3}

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