3a(a+4)-2a+7=0

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Solution for 3a(a+4)-2a+7=0 equation:


Simplifying
3a(a + 4) + -2a + 7 = 0

Reorder the terms:
3a(4 + a) + -2a + 7 = 0
(4 * 3a + a * 3a) + -2a + 7 = 0
(12a + 3a2) + -2a + 7 = 0

Reorder the terms:
7 + 12a + -2a + 3a2 = 0

Combine like terms: 12a + -2a = 10a
7 + 10a + 3a2 = 0

Solving
7 + 10a + 3a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(7 + 3a)(1 + a) = 0

Subproblem 1

Set the factor '(7 + 3a)' equal to zero and attempt to solve: Simplifying 7 + 3a = 0 Solving 7 + 3a = 0 Move all terms containing a to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + 3a = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 3a = 0 + -7 3a = 0 + -7 Combine like terms: 0 + -7 = -7 3a = -7 Divide each side by '3'. a = -2.333333333 Simplifying a = -2.333333333

Subproblem 2

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

Solution

a = {-2.333333333, -1}

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