2a^2-52-8a=32+a^2-3a

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Solution for 2a^2-52-8a=32+a^2-3a equation:


Simplifying
2a2 + -52 + -8a = 32 + a2 + -3a

Reorder the terms:
-52 + -8a + 2a2 = 32 + a2 + -3a

Reorder the terms:
-52 + -8a + 2a2 = 32 + -3a + a2

Solving
-52 + -8a + 2a2 = 32 + -3a + a2

Solving for variable 'a'.

Reorder the terms:
-52 + -32 + -8a + 3a + 2a2 + -1a2 = 32 + -3a + a2 + -32 + 3a + -1a2

Combine like terms: -52 + -32 = -84
-84 + -8a + 3a + 2a2 + -1a2 = 32 + -3a + a2 + -32 + 3a + -1a2

Combine like terms: -8a + 3a = -5a
-84 + -5a + 2a2 + -1a2 = 32 + -3a + a2 + -32 + 3a + -1a2

Combine like terms: 2a2 + -1a2 = 1a2
-84 + -5a + 1a2 = 32 + -3a + a2 + -32 + 3a + -1a2

Reorder the terms:
-84 + -5a + 1a2 = 32 + -32 + -3a + 3a + a2 + -1a2

Combine like terms: 32 + -32 = 0
-84 + -5a + 1a2 = 0 + -3a + 3a + a2 + -1a2
-84 + -5a + 1a2 = -3a + 3a + a2 + -1a2

Combine like terms: -3a + 3a = 0
-84 + -5a + 1a2 = 0 + a2 + -1a2
-84 + -5a + 1a2 = a2 + -1a2

Combine like terms: a2 + -1a2 = 0
-84 + -5a + 1a2 = 0

Factor a trinomial.
(-7 + -1a)(12 + -1a) = 0

Subproblem 1

Set the factor '(-7 + -1a)' equal to zero and attempt to solve: Simplifying -7 + -1a = 0 Solving -7 + -1a = 0 Move all terms containing a to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + -1a = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -1a = 0 + 7 -1a = 0 + 7 Combine like terms: 0 + 7 = 7 -1a = 7 Divide each side by '-1'. a = -7 Simplifying a = -7

Subproblem 2

Set the factor '(12 + -1a)' equal to zero and attempt to solve: Simplifying 12 + -1a = 0 Solving 12 + -1a = 0 Move all terms containing a to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + -1a = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -1a = 0 + -12 -1a = 0 + -12 Combine like terms: 0 + -12 = -12 -1a = -12 Divide each side by '-1'. a = 12 Simplifying a = 12

Solution

a = {-7, 12}

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