(a-1)(4a-5)=a(2a+2)

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Solution for (a-1)(4a-5)=a(2a+2) equation:


Simplifying
(a + -1)(4a + -5) = a(2a + 2)

Reorder the terms:
(-1 + a)(4a + -5) = a(2a + 2)

Reorder the terms:
(-1 + a)(-5 + 4a) = a(2a + 2)

Multiply (-1 + a) * (-5 + 4a)
(-1(-5 + 4a) + a(-5 + 4a)) = a(2a + 2)
((-5 * -1 + 4a * -1) + a(-5 + 4a)) = a(2a + 2)
((5 + -4a) + a(-5 + 4a)) = a(2a + 2)
(5 + -4a + (-5 * a + 4a * a)) = a(2a + 2)
(5 + -4a + (-5a + 4a2)) = a(2a + 2)

Combine like terms: -4a + -5a = -9a
(5 + -9a + 4a2) = a(2a + 2)

Reorder the terms:
5 + -9a + 4a2 = a(2 + 2a)
5 + -9a + 4a2 = (2 * a + 2a * a)
5 + -9a + 4a2 = (2a + 2a2)

Solving
5 + -9a + 4a2 = 2a + 2a2

Solving for variable 'a'.

Reorder the terms:
5 + -9a + -2a + 4a2 + -2a2 = 2a + 2a2 + -2a + -2a2

Combine like terms: -9a + -2a = -11a
5 + -11a + 4a2 + -2a2 = 2a + 2a2 + -2a + -2a2

Combine like terms: 4a2 + -2a2 = 2a2
5 + -11a + 2a2 = 2a + 2a2 + -2a + -2a2

Reorder the terms:
5 + -11a + 2a2 = 2a + -2a + 2a2 + -2a2

Combine like terms: 2a + -2a = 0
5 + -11a + 2a2 = 0 + 2a2 + -2a2
5 + -11a + 2a2 = 2a2 + -2a2

Combine like terms: 2a2 + -2a2 = 0
5 + -11a + 2a2 = 0

Factor a trinomial.
(1 + -2a)(5 + -1a) = 0

Subproblem 1

Set the factor '(1 + -2a)' equal to zero and attempt to solve: Simplifying 1 + -2a = 0 Solving 1 + -2a = 0 Move all terms containing a to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -2a = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2a = 0 + -1 -2a = 0 + -1 Combine like terms: 0 + -1 = -1 -2a = -1 Divide each side by '-2'. a = 0.5 Simplifying a = 0.5

Subproblem 2

Set the factor '(5 + -1a)' equal to zero and attempt to solve: Simplifying 5 + -1a = 0 Solving 5 + -1a = 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 + -1a = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1a = 0 + -5 -1a = 0 + -5 Combine like terms: 0 + -5 = -5 -1a = -5 Divide each side by '-1'. a = 5 Simplifying a = 5

Solution

a = {0.5, 5}

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