3x-9=2x^2-9

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Solution for 3x-9=2x^2-9 equation:


Simplifying
3x + -9 = 2x2 + -9

Reorder the terms:
-9 + 3x = 2x2 + -9

Reorder the terms:
-9 + 3x = -9 + 2x2

Add '9' to each side of the equation.
-9 + 9 + 3x = -9 + 9 + 2x2

Combine like terms: -9 + 9 = 0
0 + 3x = -9 + 9 + 2x2
3x = -9 + 9 + 2x2

Combine like terms: -9 + 9 = 0
3x = 0 + 2x2
3x = 2x2

Solving
3x = 2x2

Solving for variable 'x'.

Combine like terms: 2x2 + -2x2 = 0
3x + -2x2 = 0

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

Subproblem 1

Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0

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 = {0, 1.5}

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