9x^2+6x=3x+6

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


Simplifying
9x2 + 6x = 3x + 6

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

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

Solving
6x + 9x2 = 6 + 3x

Solving for variable 'x'.

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

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

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

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

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

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

Factor a trinomial.
3((-1 + -1x)(2 + -3x)) = 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 '(2 + -3x)' equal to zero and attempt to solve: Simplifying 2 + -3x = 0 Solving 2 + -3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -3x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3x = 0 + -2 -3x = 0 + -2 Combine like terms: 0 + -2 = -2 -3x = -2 Divide each side by '-3'. x = 0.6666666667 Simplifying x = 0.6666666667

Solution

x = {-1, 0.6666666667}

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