(2a-13)(5a+1)=0

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Solution for (2a-13)(5a+1)=0 equation:


Simplifying
(2a + -13)(5a + 1) = 0

Reorder the terms:
(-13 + 2a)(5a + 1) = 0

Reorder the terms:
(-13 + 2a)(1 + 5a) = 0

Multiply (-13 + 2a) * (1 + 5a)
(-13(1 + 5a) + 2a * (1 + 5a)) = 0
((1 * -13 + 5a * -13) + 2a * (1 + 5a)) = 0
((-13 + -65a) + 2a * (1 + 5a)) = 0
(-13 + -65a + (1 * 2a + 5a * 2a)) = 0
(-13 + -65a + (2a + 10a2)) = 0

Combine like terms: -65a + 2a = -63a
(-13 + -63a + 10a2) = 0

Solving
-13 + -63a + 10a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-1 + -5a)(13 + -2a) = 0

Subproblem 1

Set the factor '(-1 + -5a)' equal to zero and attempt to solve: Simplifying -1 + -5a = 0 Solving -1 + -5a = 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 + -5a = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -5a = 0 + 1 -5a = 0 + 1 Combine like terms: 0 + 1 = 1 -5a = 1 Divide each side by '-5'. a = -0.2 Simplifying a = -0.2

Subproblem 2

Set the factor '(13 + -2a)' equal to zero and attempt to solve: Simplifying 13 + -2a = 0 Solving 13 + -2a = 0 Move all terms containing a to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + -2a = 0 + -13 Combine like terms: 13 + -13 = 0 0 + -2a = 0 + -13 -2a = 0 + -13 Combine like terms: 0 + -13 = -13 -2a = -13 Divide each side by '-2'. a = 6.5 Simplifying a = 6.5

Solution

a = {-0.2, 6.5}

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