6(a-1)(a-1)-15(a-1)-9=0

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Solution for 6(a-1)(a-1)-15(a-1)-9=0 equation:


Simplifying
6(a + -1)(a + -1) + -15(a + -1) + -9 = 0

Reorder the terms:
6(-1 + a)(a + -1) + -15(a + -1) + -9 = 0

Reorder the terms:
6(-1 + a)(-1 + a) + -15(a + -1) + -9 = 0

Multiply (-1 + a) * (-1 + a)
6(-1(-1 + a) + a(-1 + a)) + -15(a + -1) + -9 = 0
6((-1 * -1 + a * -1) + a(-1 + a)) + -15(a + -1) + -9 = 0
6((1 + -1a) + a(-1 + a)) + -15(a + -1) + -9 = 0
6(1 + -1a + (-1 * a + a * a)) + -15(a + -1) + -9 = 0
6(1 + -1a + (-1a + a2)) + -15(a + -1) + -9 = 0

Combine like terms: -1a + -1a = -2a
6(1 + -2a + a2) + -15(a + -1) + -9 = 0
(1 * 6 + -2a * 6 + a2 * 6) + -15(a + -1) + -9 = 0
(6 + -12a + 6a2) + -15(a + -1) + -9 = 0

Reorder the terms:
6 + -12a + 6a2 + -15(-1 + a) + -9 = 0
6 + -12a + 6a2 + (-1 * -15 + a * -15) + -9 = 0
6 + -12a + 6a2 + (15 + -15a) + -9 = 0

Reorder the terms:
6 + 15 + -9 + -12a + -15a + 6a2 = 0

Combine like terms: 6 + 15 = 21
21 + -9 + -12a + -15a + 6a2 = 0

Combine like terms: 21 + -9 = 12
12 + -12a + -15a + 6a2 = 0

Combine like terms: -12a + -15a = -27a
12 + -27a + 6a2 = 0

Solving
12 + -27a + 6a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '3'.
3(4 + -9a + 2a2) = 0

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

Ignore the factor 3.

Subproblem 1

Set the factor '(1 + -2a)' equal to zero and attempt to solve: Simplifying 1 + -2a = 0 Solving 1 + -2a = 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 + -2a = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2a = 0 + -1 -2a = 0 + -1 Combine like terms: 0 + -1 = -1 -2a = -1 Divide each side by '-2'. a = 0.5 Simplifying a = 0.5

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 = {0.5, 4}

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