17a^2-10a=15-8a^2

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Solution for 17a^2-10a=15-8a^2 equation:


Simplifying
17a2 + -10a = 15 + -8a2

Reorder the terms:
-10a + 17a2 = 15 + -8a2

Solving
-10a + 17a2 = 15 + -8a2

Solving for variable 'a'.

Reorder the terms:
-15 + -10a + 17a2 + 8a2 = 15 + -8a2 + -15 + 8a2

Combine like terms: 17a2 + 8a2 = 25a2
-15 + -10a + 25a2 = 15 + -8a2 + -15 + 8a2

Reorder the terms:
-15 + -10a + 25a2 = 15 + -15 + -8a2 + 8a2

Combine like terms: 15 + -15 = 0
-15 + -10a + 25a2 = 0 + -8a2 + 8a2
-15 + -10a + 25a2 = -8a2 + 8a2

Combine like terms: -8a2 + 8a2 = 0
-15 + -10a + 25a2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-3 + -2a + 5a2) = 0

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

Ignore the factor 5.

Subproblem 1

Set the factor '(-3 + -5a)' equal to zero and attempt to solve: Simplifying -3 + -5a = 0 Solving -3 + -5a = 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 + -5a = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -5a = 0 + 3 -5a = 0 + 3 Combine like terms: 0 + 3 = 3 -5a = 3 Divide each side by '-5'. a = -0.6 Simplifying a = -0.6

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 = {-0.6, 1}

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