9x^2=33x-30

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Solution for 9x^2=33x-30 equation:


Simplifying
9x2 = 33x + -30

Reorder the terms:
9x2 = -30 + 33x

Solving
9x2 = -30 + 33x

Solving for variable 'x'.

Reorder the terms:
30 + -33x + 9x2 = -30 + 33x + 30 + -33x

Reorder the terms:
30 + -33x + 9x2 = -30 + 30 + 33x + -33x

Combine like terms: -30 + 30 = 0
30 + -33x + 9x2 = 0 + 33x + -33x
30 + -33x + 9x2 = 33x + -33x

Combine like terms: 33x + -33x = 0
30 + -33x + 9x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(10 + -11x + 3x2) = 0

Factor a trinomial.
3((5 + -3x)(2 + -1x)) = 0

Ignore the factor 3.

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 '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 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 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2

Solution

x = {1.666666667, 2}

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