(2a-4)(7-3a)=(5+2a)(2a-4)

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Solution for (2a-4)(7-3a)=(5+2a)(2a-4) equation: 


Simplifying
(2a + -4)(7 + -3a) = (5 + 2a)(2a + -4)

Reorder the terms:
(-4 + 2a)(7 + -3a) = (5 + 2a)(2a + -4)

Multiply (-4 + 2a) * (7 + -3a)
(-4(7 + -3a) + 2a * (7 + -3a)) = (5 + 2a)(2a + -4)
((7 * -4 + -3a * -4) + 2a * (7 + -3a)) = (5 + 2a)(2a + -4)
((-28 + 12a) + 2a * (7 + -3a)) = (5 + 2a)(2a + -4)
(-28 + 12a + (7 * 2a + -3a * 2a)) = (5 + 2a)(2a + -4)
(-28 + 12a + (14a + -6a2)) = (5 + 2a)(2a + -4)

Combine like terms: 12a + 14a = 26a
(-28 + 26a + -6a2) = (5 + 2a)(2a + -4)

Reorder the terms:
-28 + 26a + -6a2 = (5 + 2a)(-4 + 2a)

Multiply (5 + 2a) * (-4 + 2a)
-28 + 26a + -6a2 = (5(-4 + 2a) + 2a * (-4 + 2a))
-28 + 26a + -6a2 = ((-4 * 5 + 2a * 5) + 2a * (-4 + 2a))
-28 + 26a + -6a2 = ((-20 + 10a) + 2a * (-4 + 2a))
-28 + 26a + -6a2 = (-20 + 10a + (-4 * 2a + 2a * 2a))
-28 + 26a + -6a2 = (-20 + 10a + (-8a + 4a2))

Combine like terms: 10a + -8a = 2a
-28 + 26a + -6a2 = (-20 + 2a + 4a2)

Solving
-28 + 26a + -6a2 = -20 + 2a + 4a2

Solving for variable 'a'.

Reorder the terms:
-28 + 20 + 26a + -2a + -6a2 + -4a2 = -20 + 2a + 4a2 + 20 + -2a + -4a2

Combine like terms: -28 + 20 = -8
-8 + 26a + -2a + -6a2 + -4a2 = -20 + 2a + 4a2 + 20 + -2a + -4a2

Combine like terms: 26a + -2a = 24a
-8 + 24a + -6a2 + -4a2 = -20 + 2a + 4a2 + 20 + -2a + -4a2

Combine like terms: -6a2 + -4a2 = -10a2
-8 + 24a + -10a2 = -20 + 2a + 4a2 + 20 + -2a + -4a2

Reorder the terms:
-8 + 24a + -10a2 = -20 + 20 + 2a + -2a + 4a2 + -4a2

Combine like terms: -20 + 20 = 0
-8 + 24a + -10a2 = 0 + 2a + -2a + 4a2 + -4a2
-8 + 24a + -10a2 = 2a + -2a + 4a2 + -4a2

Combine like terms: 2a + -2a = 0
-8 + 24a + -10a2 = 0 + 4a2 + -4a2
-8 + 24a + -10a2 = 4a2 + -4a2

Combine like terms: 4a2 + -4a2 = 0
-8 + 24a + -10a2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-4 + 12a + -5a2) = 0

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

Ignore the factor 2.

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

Simplifying
-2 + a = 0

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

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

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

Simplifying
a = 2

Subproblem 2
Set the factor '(2 + -5a)' equal to zero and attempt to solve:

Simplifying
2 + -5a = 0

Solving
2 + -5a = 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 + -5a = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -5a = 0 + -2
-5a = 0 + -2

Combine like terms: 0 + -2 = -2
-5a = -2

Divide each side by '-5'.
a = 0.4

Simplifying
a = 0.4
Solution
a = {2, 0.4}

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