5a^2=-8a-3

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Solution for 5a^2=-8a-3 equation:


Simplifying
5a2 = -8a + -3

Reorder the terms:
5a2 = -3 + -8a

Solving
5a2 = -3 + -8a

Solving for variable 'a'.

Reorder the terms:
3 + 8a + 5a2 = -3 + -8a + 3 + 8a

Reorder the terms:
3 + 8a + 5a2 = -3 + 3 + -8a + 8a

Combine like terms: -3 + 3 = 0
3 + 8a + 5a2 = 0 + -8a + 8a
3 + 8a + 5a2 = -8a + 8a

Combine like terms: -8a + 8a = 0
3 + 8a + 5a2 = 0

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

Subproblem 1

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

Subproblem 2

Set the factor '(3 + 5a)' equal to zero and attempt to solve: Simplifying 3 + 5a = 0 Solving 3 + 5a = 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 + 5a = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 5a = 0 + -3 5a = 0 + -3 Combine like terms: 0 + -3 = -3 5a = -3 Divide each side by '5'. a = -0.6 Simplifying a = -0.6

Solution

a = {-1, -0.6}

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