(2a-5)(3a+7)=0

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Solution for (2a-5)(3a+7)=0 equation: 


Simplifying
(2a + -5)(3a + 7) = 0

Reorder the terms:
(-5 + 2a)(3a + 7) = 0

Reorder the terms:
(-5 + 2a)(7 + 3a) = 0

Multiply (-5 + 2a) * (7 + 3a)
(-5(7 + 3a) + 2a * (7 + 3a)) = 0
((7 * -5 + 3a * -5) + 2a * (7 + 3a)) = 0
((-35 + -15a) + 2a * (7 + 3a)) = 0
(-35 + -15a + (7 * 2a + 3a * 2a)) = 0
(-35 + -15a + (14a + 6a2)) = 0

Combine like terms: -15a + 14a = -1a
(-35 + -1a + 6a2) = 0

Solving
-35 + -1a + 6a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-7 + -3a)(5 + -2a) = 0


Subproblem 1
Set the factor '(-7 + -3a)' equal to zero and attempt to solve:

Simplifying
-7 + -3a = 0

Solving
-7 + -3a = 0

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

Add '7' to each side of the equation.
-7 + 7 + -3a = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -3a = 0 + 7
-3a = 0 + 7

Combine like terms: 0 + 7 = 7
-3a = 7

Divide each side by '-3'.
a = -2.333333333

Simplifying
a = -2.333333333

Subproblem 2
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
Solution
a = {-2.333333333, 2.5}

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