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

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Solution for (2a-3)*(5-2a)-(1-2a)*(1+2a)=0 equation:


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

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

Multiply (-3 + 2a) * (5 + -2a)
(-3(5 + -2a) + 2a * (5 + -2a)) + -1(1 + -2a)(1 + 2a) = 0
((5 * -3 + -2a * -3) + 2a * (5 + -2a)) + -1(1 + -2a)(1 + 2a) = 0
((-15 + 6a) + 2a * (5 + -2a)) + -1(1 + -2a)(1 + 2a) = 0
(-15 + 6a + (5 * 2a + -2a * 2a)) + -1(1 + -2a)(1 + 2a) = 0
(-15 + 6a + (10a + -4a2)) + -1(1 + -2a)(1 + 2a) = 0

Combine like terms: 6a + 10a = 16a
(-15 + 16a + -4a2) + -1(1 + -2a)(1 + 2a) = 0

Multiply (1 + -2a) * (1 + 2a)
-15 + 16a + -4a2 + -1(1(1 + 2a) + -2a * (1 + 2a)) = 0
-15 + 16a + -4a2 + -1((1 * 1 + 2a * 1) + -2a * (1 + 2a)) = 0
-15 + 16a + -4a2 + -1((1 + 2a) + -2a * (1 + 2a)) = 0
-15 + 16a + -4a2 + -1(1 + 2a + (1 * -2a + 2a * -2a)) = 0
-15 + 16a + -4a2 + -1(1 + 2a + (-2a + -4a2)) = 0

Combine like terms: 2a + -2a = 0
-15 + 16a + -4a2 + -1(1 + 0 + -4a2) = 0
-15 + 16a + -4a2 + -1(1 + -4a2) = 0
-15 + 16a + -4a2 + (1 * -1 + -4a2 * -1) = 0
-15 + 16a + -4a2 + (-1 + 4a2) = 0

Reorder the terms:
-15 + -1 + 16a + -4a2 + 4a2 = 0

Combine like terms: -15 + -1 = -16
-16 + 16a + -4a2 + 4a2 = 0

Combine like terms: -4a2 + 4a2 = 0
-16 + 16a + 0 = 0
-16 + 16a = 0

Solving
-16 + 16a = 0

Solving for variable 'a'.

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

Add '16' to each side of the equation.
-16 + 16 + 16a = 0 + 16

Combine like terms: -16 + 16 = 0
0 + 16a = 0 + 16
16a = 0 + 16

Combine like terms: 0 + 16 = 16
16a = 16

Divide each side by '16'.
a = 1

Simplifying
a = 1

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