a(a-x)+3a(x+2)-a(x-3a)=

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Solution for a(a-x)+3a(x+2)-a(x-3a)= equation:


Simplifying
a(a + -1x) + 3a(x + 2) + -1a(x + -3a) = 0
(a * a + -1x * a) + 3a(x + 2) + -1a(x + -3a) = 0

Reorder the terms:
(-1ax + a2) + 3a(x + 2) + -1a(x + -3a) = 0
(-1ax + a2) + 3a(x + 2) + -1a(x + -3a) = 0

Reorder the terms:
-1ax + a2 + 3a(2 + x) + -1a(x + -3a) = 0
-1ax + a2 + (2 * 3a + x * 3a) + -1a(x + -3a) = 0
-1ax + a2 + (6a + 3ax) + -1a(x + -3a) = 0

Reorder the terms:
-1ax + a2 + 6a + 3ax + -1a(-3a + x) = 0
-1ax + a2 + 6a + 3ax + (-3a * -1a + x * -1a) = 0

Reorder the terms:
-1ax + a2 + 6a + 3ax + (-1ax + 3a2) = 0
-1ax + a2 + 6a + 3ax + (-1ax + 3a2) = 0

Reorder the terms:
6a + -1ax + 3ax + -1ax + a2 + 3a2 = 0

Combine like terms: -1ax + 3ax = 2ax
6a + 2ax + -1ax + a2 + 3a2 = 0

Combine like terms: 2ax + -1ax = 1ax
6a + 1ax + a2 + 3a2 = 0

Combine like terms: a2 + 3a2 = 4a2
6a + 1ax + 4a2 = 0

Solving
6a + 1ax + 4a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), 'a'.
a(6 + x + 4a) = 0

Subproblem 1

Set the factor 'a' equal to zero and attempt to solve: Simplifying a = 0 Solving a = 0 Move all terms containing a to the left, all other terms to the right. Simplifying a = 0

Subproblem 2

Set the factor '(6 + x + 4a)' equal to zero and attempt to solve: Simplifying 6 + x + 4a = 0 Reorder the terms: 6 + 4a + x = 0 Solving 6 + 4a + x = 0 Move all terms containing a to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + 4a + -6 + x = 0 + -6 Reorder the terms: 6 + -6 + 4a + x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + 4a + x = 0 + -6 4a + x = 0 + -6 Combine like terms: 0 + -6 = -6 4a + x = -6 Add '-1x' to each side of the equation. 4a + x + -1x = -6 + -1x Combine like terms: x + -1x = 0 4a + 0 = -6 + -1x 4a = -6 + -1x Divide each side by '4'. a = -1.5 + -0.25x Simplifying a = -1.5 + -0.25x

Solution

a = {0, -1.5 + -0.25x}

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