(5a-1)(2a+3)=

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Solution for (5a-1)(2a+3)= equation:


Simplifying
(5a + -1)(2a + 3) = 0

Reorder the terms:
(-1 + 5a)(2a + 3) = 0

Reorder the terms:
(-1 + 5a)(3 + 2a) = 0

Multiply (-1 + 5a) * (3 + 2a)
(-1(3 + 2a) + 5a * (3 + 2a)) = 0
((3 * -1 + 2a * -1) + 5a * (3 + 2a)) = 0
((-3 + -2a) + 5a * (3 + 2a)) = 0
(-3 + -2a + (3 * 5a + 2a * 5a)) = 0
(-3 + -2a + (15a + 10a2)) = 0

Combine like terms: -2a + 15a = 13a
(-3 + 13a + 10a2) = 0

Solving
-3 + 13a + 10a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-3 + -2a)(1 + -5a) = 0

Subproblem 1

Set the factor '(-3 + -2a)' equal to zero and attempt to solve: Simplifying -3 + -2a = 0 Solving -3 + -2a = 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 + -2a = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -2a = 0 + 3 -2a = 0 + 3 Combine like terms: 0 + 3 = 3 -2a = 3 Divide each side by '-2'. a = -1.5 Simplifying a = -1.5

Subproblem 2

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

Solution

a = {-1.5, 0.2}

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