10a^2+41a=-4

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Solution for 10a^2+41a=-4 equation:


Simplifying
10a2 + 41a = -4

Reorder the terms:
41a + 10a2 = -4

Solving
41a + 10a2 = -4

Solving for variable 'a'.

Reorder the terms:
4 + 41a + 10a2 = -4 + 4

Combine like terms: -4 + 4 = 0
4 + 41a + 10a2 = 0

Factor a trinomial.
(4 + a)(1 + 10a) = 0

Subproblem 1

Set the factor '(4 + a)' equal to zero and attempt to solve: Simplifying 4 + a = 0 Solving 4 + a = 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 + a = 0 + -4 Combine like terms: 4 + -4 = 0 0 + a = 0 + -4 a = 0 + -4 Combine like terms: 0 + -4 = -4 a = -4 Simplifying a = -4

Subproblem 2

Set the factor '(1 + 10a)' equal to zero and attempt to solve: Simplifying 1 + 10a = 0 Solving 1 + 10a = 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 + 10a = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 10a = 0 + -1 10a = 0 + -1 Combine like terms: 0 + -1 = -1 10a = -1 Divide each side by '10'. a = -0.1 Simplifying a = -0.1

Solution

a = {-4, -0.1}

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