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

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


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

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

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

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

Combine like terms: -2a + 1a = -1a
(-2 + -1a + a2) = -2a

Solving
-2 + -1a + a2 = -2a

Solving for variable 'a'.

Reorder the terms:
-2 + -1a + 2a + a2 = -2a + 2a

Combine like terms: -1a + 2a = 1a
-2 + 1a + a2 = -2a + 2a

Combine like terms: -2a + 2a = 0
-2 + 1a + a2 = 0

Factor a trinomial.
(-2 + -1a)(1 + -1a) = 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 '(1 + -1a)' equal to zero and attempt to solve: Simplifying 1 + -1a = 0 Solving 1 + -1a = 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 + -1a = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1a = 0 + -1 -1a = 0 + -1 Combine like terms: 0 + -1 = -1 -1a = -1 Divide each side by '-1'. a = 1 Simplifying a = 1

Solution

a = {-2, 1}

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