7a(4a+a)=8(1a+a)

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Solution for 7a(4a+a)=8(1a+a) equation:


Simplifying
7a(4a + a) = 8(1a + a)

Combine like terms: 4a + a = 5a
7a(5a) = 8(1a + a)

Remove parenthesis around (5a)
7a * 5a = 8(1a + a)

Reorder the terms for easier multiplication:
7 * 5a * a = 8(1a + a)

Multiply 7 * 5
35a * a = 8(1a + a)

Multiply a * a
35a2 = 8(1a + a)

Combine like terms: 1a + a = 2a
35a2 = 8(2a)

Remove parenthesis around (2a)
35a2 = 8 * 2a

Multiply 8 * 2
35a2 = 16a

Solving
35a2 = 16a

Solving for variable 'a'.

Reorder the terms:
-16a + 35a2 = 16a + -16a

Combine like terms: 16a + -16a = 0
-16a + 35a2 = 0

Factor out the Greatest Common Factor (GCF), 'a'.
a(-16 + 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 '(-16 + 35a)' equal to zero and attempt to solve: Simplifying -16 + 35a = 0 Solving -16 + 35a = 0 Move all terms containing a to the left, all other terms to the right. Add '16' to each side of the equation. -16 + 16 + 35a = 0 + 16 Combine like terms: -16 + 16 = 0 0 + 35a = 0 + 16 35a = 0 + 16 Combine like terms: 0 + 16 = 16 35a = 16 Divide each side by '35'. a = 0.4571428571 Simplifying a = 0.4571428571

Solution

a = {0, 0.4571428571}

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