a(a+5)=29a-144

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Solution for a(a+5)=29a-144 equation:


Simplifying
a(a + 5) = 29a + -144

Reorder the terms:
a(5 + a) = 29a + -144
(5 * a + a * a) = 29a + -144
(5a + a2) = 29a + -144

Reorder the terms:
5a + a2 = -144 + 29a

Solving
5a + a2 = -144 + 29a

Solving for variable 'a'.

Reorder the terms:
144 + 5a + -29a + a2 = -144 + 29a + 144 + -29a

Combine like terms: 5a + -29a = -24a
144 + -24a + a2 = -144 + 29a + 144 + -29a

Reorder the terms:
144 + -24a + a2 = -144 + 144 + 29a + -29a

Combine like terms: -144 + 144 = 0
144 + -24a + a2 = 0 + 29a + -29a
144 + -24a + a2 = 29a + -29a

Combine like terms: 29a + -29a = 0
144 + -24a + a2 = 0

Factor a trinomial.
(12 + -1a)(12 + -1a) = 0

Subproblem 1

Set the factor '(12 + -1a)' equal to zero and attempt to solve: Simplifying 12 + -1a = 0 Solving 12 + -1a = 0 Move all terms containing a to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + -1a = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -1a = 0 + -12 -1a = 0 + -12 Combine like terms: 0 + -12 = -12 -1a = -12 Divide each side by '-1'. a = 12 Simplifying a = 12

Subproblem 2

Set the factor '(12 + -1a)' equal to zero and attempt to solve: Simplifying 12 + -1a = 0 Solving 12 + -1a = 0 Move all terms containing a to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + -1a = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -1a = 0 + -12 -1a = 0 + -12 Combine like terms: 0 + -12 = -12 -1a = -12 Divide each side by '-1'. a = 12 Simplifying a = 12

Solution

a = {12, 12}

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