-4a(a-7)=-10a(4a+5)

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Solution for -4a(a-7)=-10a(4a+5) equation:


Simplifying
-4a(a + -7) = -10a(4a + 5)

Reorder the terms:
-4a(-7 + a) = -10a(4a + 5)
(-7 * -4a + a * -4a) = -10a(4a + 5)
(28a + -4a2) = -10a(4a + 5)

Reorder the terms:
28a + -4a2 = -10a(5 + 4a)
28a + -4a2 = (5 * -10a + 4a * -10a)
28a + -4a2 = (-50a + -40a2)

Solving
28a + -4a2 = -50a + -40a2

Solving for variable 'a'.

Reorder the terms:
28a + 50a + -4a2 + 40a2 = -50a + -40a2 + 50a + 40a2

Combine like terms: 28a + 50a = 78a
78a + -4a2 + 40a2 = -50a + -40a2 + 50a + 40a2

Combine like terms: -4a2 + 40a2 = 36a2
78a + 36a2 = -50a + -40a2 + 50a + 40a2

Reorder the terms:
78a + 36a2 = -50a + 50a + -40a2 + 40a2

Combine like terms: -50a + 50a = 0
78a + 36a2 = 0 + -40a2 + 40a2
78a + 36a2 = -40a2 + 40a2

Combine like terms: -40a2 + 40a2 = 0
78a + 36a2 = 0

Factor out the Greatest Common Factor (GCF), '6a'.
6a(13 + 6a) = 0

Ignore the factor 6.

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 '(13 + 6a)' equal to zero and attempt to solve: Simplifying 13 + 6a = 0 Solving 13 + 6a = 0 Move all terms containing a to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + 6a = 0 + -13 Combine like terms: 13 + -13 = 0 0 + 6a = 0 + -13 6a = 0 + -13 Combine like terms: 0 + -13 = -13 6a = -13 Divide each side by '6'. a = -2.166666667 Simplifying a = -2.166666667

Solution

a = {0, -2.166666667}

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