(-2a+3)(3a-6)=0

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Solution for (-2a+3)(3a-6)=0 equation:


Simplifying
(-2a + 3)(3a + -6) = 0

Reorder the terms:
(3 + -2a)(3a + -6) = 0

Reorder the terms:
(3 + -2a)(-6 + 3a) = 0

Multiply (3 + -2a) * (-6 + 3a)
(3(-6 + 3a) + -2a * (-6 + 3a)) = 0
((-6 * 3 + 3a * 3) + -2a * (-6 + 3a)) = 0
((-18 + 9a) + -2a * (-6 + 3a)) = 0
(-18 + 9a + (-6 * -2a + 3a * -2a)) = 0
(-18 + 9a + (12a + -6a2)) = 0

Combine like terms: 9a + 12a = 21a
(-18 + 21a + -6a2) = 0

Solving
-18 + 21a + -6a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-6 + 7a + -2a2) = 0

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

Ignore the factor 3.

Subproblem 1

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

Subproblem 2

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

Solution

a = {2, 1.5}

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