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

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


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

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

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

Multiply (3 + 5a) * (-7 + 2a)
(3(-7 + 2a) + 5a * (-7 + 2a)) = 0
((-7 * 3 + 2a * 3) + 5a * (-7 + 2a)) = 0
((-21 + 6a) + 5a * (-7 + 2a)) = 0
(-21 + 6a + (-7 * 5a + 2a * 5a)) = 0
(-21 + 6a + (-35a + 10a2)) = 0

Combine like terms: 6a + -35a = -29a
(-21 + -29a + 10a2) = 0

Solving
-21 + -29a + 10a2 = 0

Solving for variable 'a'.

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


Subproblem 1
Set the factor '(-3 + -5a)' equal to zero and attempt to solve:

Simplifying
-3 + -5a = 0

Solving
-3 + -5a = 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 + -5a = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -5a = 0 + 3
-5a = 0 + 3

Combine like terms: 0 + 3 = 3
-5a = 3

Divide each side by '-5'.
a = -0.6

Simplifying
a = -0.6

Subproblem 2
Set the factor '(7 + -2a)' equal to zero and attempt to solve:

Simplifying
7 + -2a = 0

Solving
7 + -2a = 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 + -2a = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -2a = 0 + -7
-2a = 0 + -7

Combine like terms: 0 + -7 = -7
-2a = -7

Divide each side by '-2'.
a = 3.5

Simplifying
a = 3.5
Solution
a = {-0.6, 3.5}

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