2(a-5)(a+5)=21a

Solution for 2(a-5)(a+5)=21a equation:

Simplifying
2(a + -5)(a + 5) = 21a

Reorder the terms:
2(-5 + a)(a + 5) = 21a

Reorder the terms:
2(-5 + a)(5 + a) = 21a

Multiply (-5 + a) * (5 + a)
2(-5(5 + a) + a(5 + a)) = 21a
2((5 * -5 + a * -5) + a(5 + a)) = 21a
2((-25 + -5a) + a(5 + a)) = 21a
2(-25 + -5a + (5 * a + a * a)) = 21a
2(-25 + -5a + (5a + a2)) = 21a

Combine like terms: -5a + 5a = 0
2(-25 + 0 + a2) = 21a
2(-25 + a2) = 21a
(-25 * 2 + a2 * 2) = 21a
(-50 + 2a2) = 21a

Solving
-50 + 2a2 = 21a

Solving for variable 'a'.

Reorder the terms:
-50 + -21a + 2a2 = 21a + -21a

Combine like terms: 21a + -21a = 0
-50 + -21a + 2a2 = 0

Factor a trinomial.
(-2 + -1a)(25 + -2a) = 0

Subproblem 1
Set the factor '(-2 + -1a)' equal to zero and attempt to solve:

Simplifying
-2 + -1a = 0

Solving
-2 + -1a = 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 + -1a = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1a = 0 + 2
-1a = 0 + 2

Combine like terms: 0 + 2 = 2
-1a = 2

Divide each side by '-1'.
a = -2

Simplifying
a = -2
Subproblem 2
Set the factor '(25 + -2a)' equal to zero and attempt to solve:

Simplifying
25 + -2a = 0

Solving
25 + -2a = 0

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

Add '-25' to each side of the equation.
25 + -25 + -2a = 0 + -25

Combine like terms: 25 + -25 = 0
0 + -2a = 0 + -25
-2a = 0 + -25

Combine like terms: 0 + -25 = -25
-2a = -25

Divide each side by '-2'.
a = 12.5

Simplifying
a = 12.5
Solution
a = {-2, 12.5}