a^2+7a-9=-3+6a

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Solution for a^2+7a-9=-3+6a equation:


Simplifying
a2 + 7a + -9 = -3 + 6a

Reorder the terms:
-9 + 7a + a2 = -3 + 6a

Solving
-9 + 7a + a2 = -3 + 6a

Solving for variable 'a'.

Reorder the terms:
-9 + 3 + 7a + -6a + a2 = -3 + 6a + 3 + -6a

Combine like terms: -9 + 3 = -6
-6 + 7a + -6a + a2 = -3 + 6a + 3 + -6a

Combine like terms: 7a + -6a = 1a
-6 + 1a + a2 = -3 + 6a + 3 + -6a

Reorder the terms:
-6 + 1a + a2 = -3 + 3 + 6a + -6a

Combine like terms: -3 + 3 = 0
-6 + 1a + a2 = 0 + 6a + -6a
-6 + 1a + a2 = 6a + -6a

Combine like terms: 6a + -6a = 0
-6 + 1a + a2 = 0

Factor a trinomial.
(-3 + -1a)(2 + -1a) = 0

Subproblem 1

Set the factor '(-3 + -1a)' equal to zero and attempt to solve: Simplifying -3 + -1a = 0 Solving -3 + -1a = 0 Move all terms containing a to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -1a = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1a = 0 + 3 -1a = 0 + 3 Combine like terms: 0 + 3 = 3 -1a = 3 Divide each side by '-1'. a = -3 Simplifying a = -3

Subproblem 2

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

Solution

a = {-3, 2}

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