7a(4a+a)=(a+a)

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Solution for 7a(4a+a)=(a+a) equation:


Simplifying
7a(4a + a) = (a + a)

Combine like terms: 4a + a = 5a
7a(5a) = (a + a)

Remove parenthesis around (5a)
7a * 5a = (a + a)

Reorder the terms for easier multiplication:
7 * 5a * a = (a + a)

Multiply 7 * 5
35a * a = (a + a)

Multiply a * a
35a2 = (a + a)

Combine like terms: a + a = 2a
35a2 = (2a)
35a2 = (2a)

Solving
35a2 = (2a)

Solving for variable 'a'.

Reorder the terms:
(-2a) + 35a2 = (2a) + (-2a)

Combine like terms: (2a) + (-2a) = 0
(-2a) + 35a2 = 0

Factor out the Greatest Common Factor (GCF), 'a'.
a(-2 + 35a) = 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 '(-2 + 35a)' equal to zero and attempt to solve: Simplifying -2 + 35a = 0 Solving -2 + 35a = 0 Move all terms containing a to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + 35a = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 35a = 0 + 2 35a = 0 + 2 Combine like terms: 0 + 2 = 2 35a = 2 Divide each side by '35'. a = 0.05714285714 Simplifying a = 0.05714285714

Solution

a = {0, 0.05714285714}

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