(2a+5)(a-11)=0

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Solution for (2a+5)(a-11)=0 equation:


Simplifying
(2a + 5)(a + -11) = 0

Reorder the terms:
(5 + 2a)(a + -11) = 0

Reorder the terms:
(5 + 2a)(-11 + a) = 0

Multiply (5 + 2a) * (-11 + a)
(5(-11 + a) + 2a * (-11 + a)) = 0
((-11 * 5 + a * 5) + 2a * (-11 + a)) = 0
((-55 + 5a) + 2a * (-11 + a)) = 0
(-55 + 5a + (-11 * 2a + a * 2a)) = 0
(-55 + 5a + (-22a + 2a2)) = 0

Combine like terms: 5a + -22a = -17a
(-55 + -17a + 2a2) = 0

Solving
-55 + -17a + 2a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-5 + -2a)(11 + -1a) = 0

Subproblem 1

Set the factor '(-5 + -2a)' equal to zero and attempt to solve: Simplifying -5 + -2a = 0 Solving -5 + -2a = 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 + -2a = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -2a = 0 + 5 -2a = 0 + 5 Combine like terms: 0 + 5 = 5 -2a = 5 Divide each side by '-2'. a = -2.5 Simplifying a = -2.5

Subproblem 2

Set the factor '(11 + -1a)' equal to zero and attempt to solve: Simplifying 11 + -1a = 0 Solving 11 + -1a = 0 Move all terms containing a to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + -1a = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -1a = 0 + -11 -1a = 0 + -11 Combine like terms: 0 + -11 = -11 -1a = -11 Divide each side by '-1'. a = 11 Simplifying a = 11

Solution

a = {-2.5, 11}

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