3a(2-2a)=10a

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Solution for 3a(2-2a)=10a equation:


Simplifying
3a(2 + -2a) = 10a
(2 * 3a + -2a * 3a) = 10a
(6a + -6a2) = 10a

Solving
6a + -6a2 = 10a

Solving for variable 'a'.

Reorder the terms:
6a + -10a + -6a2 = 10a + -10a

Combine like terms: 6a + -10a = -4a
-4a + -6a2 = 10a + -10a

Combine like terms: 10a + -10a = 0
-4a + -6a2 = 0

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

Ignore the factor -2.

Subproblem 1

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

Subproblem 2

Set the factor '(2 + 3a)' equal to zero and attempt to solve: Simplifying 2 + 3a = 0 Solving 2 + 3a = 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 + 3a = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 3a = 0 + -2 3a = 0 + -2 Combine like terms: 0 + -2 = -2 3a = -2 Divide each side by '3'. a = -0.6666666667 Simplifying a = -0.6666666667

Solution

a = {0, -0.6666666667}

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