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

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Solution for (2a+5)(3a-2)=0 equation: 


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

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

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

Multiply (5 + 2a) * (-2 + 3a)
(5(-2 + 3a) + 2a * (-2 + 3a)) = 0
((-2 * 5 + 3a * 5) + 2a * (-2 + 3a)) = 0
((-10 + 15a) + 2a * (-2 + 3a)) = 0
(-10 + 15a + (-2 * 2a + 3a * 2a)) = 0
(-10 + 15a + (-4a + 6a2)) = 0

Combine like terms: 15a + -4a = 11a
(-10 + 11a + 6a2) = 0

Solving
-10 + 11a + 6a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-5 + -2a)(2 + -3a) = 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 '(2 + -3a)' equal to zero and attempt to solve:

Simplifying
2 + -3a = 0

Solving
2 + -3a = 0

Move all terms containing a to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + -2 + -3a = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3a = 0 + -2
-3a = 0 + -2

Combine like terms: 0 + -2 = -2
-3a = -2

Divide each side by '-3'.
a = 0.6666666667

Simplifying
a = 0.6666666667
Solution
a = {-2.5, 0.6666666667}

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