3a^2=5(2a+4)-3a

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Solution for 3a^2=5(2a+4)-3a equation:


Simplifying
3a2 = 5(2a + 4) + -3a

Reorder the terms:
3a2 = 5(4 + 2a) + -3a
3a2 = (4 * 5 + 2a * 5) + -3a
3a2 = (20 + 10a) + -3a

Combine like terms: 10a + -3a = 7a
3a2 = 20 + 7a

Solving
3a2 = 20 + 7a

Solving for variable 'a'.

Reorder the terms:
-20 + -7a + 3a2 = 20 + 7a + -20 + -7a

Reorder the terms:
-20 + -7a + 3a2 = 20 + -20 + 7a + -7a

Combine like terms: 20 + -20 = 0
-20 + -7a + 3a2 = 0 + 7a + -7a
-20 + -7a + 3a2 = 7a + -7a

Combine like terms: 7a + -7a = 0
-20 + -7a + 3a2 = 0

Factor a trinomial.
(-5 + -3a)(4 + -1a) = 0

Subproblem 1

Set the factor '(-5 + -3a)' equal to zero and attempt to solve: Simplifying -5 + -3a = 0 Solving -5 + -3a = 0 Move all terms containing a to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -3a = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -3a = 0 + 5 -3a = 0 + 5 Combine like terms: 0 + 5 = 5 -3a = 5 Divide each side by '-3'. a = -1.666666667 Simplifying a = -1.666666667

Subproblem 2

Set the factor '(4 + -1a)' equal to zero and attempt to solve: Simplifying 4 + -1a = 0 Solving 4 + -1a = 0 Move all terms containing a to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1a = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1a = 0 + -4 -1a = 0 + -4 Combine like terms: 0 + -4 = -4 -1a = -4 Divide each side by '-1'. a = 4 Simplifying a = 4

Solution

a = {-1.666666667, 4}

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