12a^2=19a-5

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Solution for 12a^2=19a-5 equation:


Simplifying
12a2 = 19a + -5

Reorder the terms:
12a2 = -5 + 19a

Solving
12a2 = -5 + 19a

Solving for variable 'a'.

Reorder the terms:
5 + -19a + 12a2 = -5 + 19a + 5 + -19a

Reorder the terms:
5 + -19a + 12a2 = -5 + 5 + 19a + -19a

Combine like terms: -5 + 5 = 0
5 + -19a + 12a2 = 0 + 19a + -19a
5 + -19a + 12a2 = 19a + -19a

Combine like terms: 19a + -19a = 0
5 + -19a + 12a2 = 0

Factor a trinomial.
(1 + -3a)(5 + -4a) = 0

Subproblem 1

Set the factor '(1 + -3a)' equal to zero and attempt to solve: Simplifying 1 + -3a = 0 Solving 1 + -3a = 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 + -3a = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3a = 0 + -1 -3a = 0 + -1 Combine like terms: 0 + -1 = -1 -3a = -1 Divide each side by '-3'. a = 0.3333333333 Simplifying a = 0.3333333333

Subproblem 2

Set the factor '(5 + -4a)' equal to zero and attempt to solve: Simplifying 5 + -4a = 0 Solving 5 + -4a = 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 + -4a = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -4a = 0 + -5 -4a = 0 + -5 Combine like terms: 0 + -5 = -5 -4a = -5 Divide each side by '-4'. a = 1.25 Simplifying a = 1.25

Solution

a = {0.3333333333, 1.25}

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