2a^2=5a+12

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Solution for 2a^2=5a+12 equation:


Simplifying
2a2 = 5a + 12

Reorder the terms:
2a2 = 12 + 5a

Solving
2a2 = 12 + 5a

Solving for variable 'a'.

Reorder the terms:
-12 + -5a + 2a2 = 12 + 5a + -12 + -5a

Reorder the terms:
-12 + -5a + 2a2 = 12 + -12 + 5a + -5a

Combine like terms: 12 + -12 = 0
-12 + -5a + 2a2 = 0 + 5a + -5a
-12 + -5a + 2a2 = 5a + -5a

Combine like terms: 5a + -5a = 0
-12 + -5a + 2a2 = 0

Factor a trinomial.
(-3 + -2a)(4 + -1a) = 0

Subproblem 1

Set the factor '(-3 + -2a)' equal to zero and attempt to solve: Simplifying -3 + -2a = 0 Solving -3 + -2a = 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 + -2a = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -2a = 0 + 3 -2a = 0 + 3 Combine like terms: 0 + 3 = 3 -2a = 3 Divide each side by '-2'. a = -1.5 Simplifying a = -1.5

Subproblem 2

Set the factor '(4 + -1a)' equal to zero and attempt to solve: Simplifying 4 + -1a = 0 Solving 4 + -1a = 0 Move all terms containing a to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1a = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1a = 0 + -4 -1a = 0 + -4 Combine like terms: 0 + -4 = -4 -1a = -4 Divide each side by '-1'. a = 4 Simplifying a = 4

Solution

a = {-1.5, 4}

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