3a(a-5)=7(a+5)(a+2)-70

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Solution for 3a(a-5)=7(a+5)(a+2)-70 equation: 


Simplifying
3a(a + -5) = 7(a + 5)(a + 2) + -70

Reorder the terms:
3a(-5 + a) = 7(a + 5)(a + 2) + -70
(-5 * 3a + a * 3a) = 7(a + 5)(a + 2) + -70
(-15a + 3a2) = 7(a + 5)(a + 2) + -70

Reorder the terms:
-15a + 3a2 = 7(5 + a)(a + 2) + -70

Reorder the terms:
-15a + 3a2 = 7(5 + a)(2 + a) + -70

Multiply (5 + a) * (2 + a)
-15a + 3a2 = 7(5(2 + a) + a(2 + a)) + -70
-15a + 3a2 = 7((2 * 5 + a * 5) + a(2 + a)) + -70
-15a + 3a2 = 7((10 + 5a) + a(2 + a)) + -70
-15a + 3a2 = 7(10 + 5a + (2 * a + a * a)) + -70
-15a + 3a2 = 7(10 + 5a + (2a + a2)) + -70

Combine like terms: 5a + 2a = 7a
-15a + 3a2 = 7(10 + 7a + a2) + -70
-15a + 3a2 = (10 * 7 + 7a * 7 + a2 * 7) + -70
-15a + 3a2 = (70 + 49a + 7a2) + -70

Reorder the terms:
-15a + 3a2 = 70 + -70 + 49a + 7a2

Combine like terms: 70 + -70 = 0
-15a + 3a2 = 0 + 49a + 7a2
-15a + 3a2 = 49a + 7a2

Solving
-15a + 3a2 = 49a + 7a2

Solving for variable 'a'.

Reorder the terms:
-15a + -49a + 3a2 + -7a2 = 49a + 7a2 + -49a + -7a2

Combine like terms: -15a + -49a = -64a
-64a + 3a2 + -7a2 = 49a + 7a2 + -49a + -7a2

Combine like terms: 3a2 + -7a2 = -4a2
-64a + -4a2 = 49a + 7a2 + -49a + -7a2

Reorder the terms:
-64a + -4a2 = 49a + -49a + 7a2 + -7a2

Combine like terms: 49a + -49a = 0
-64a + -4a2 = 0 + 7a2 + -7a2
-64a + -4a2 = 7a2 + -7a2

Combine like terms: 7a2 + -7a2 = 0
-64a + -4a2 = 0

Factor out the Greatest Common Factor (GCF), '-4a'.
-4a(16 + a) = 0

Ignore the factor -4.

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 + a)' equal to zero and attempt to solve:

Simplifying
16 + a = 0

Solving
16 + a = 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 + a = 0 + -16

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

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

Simplifying
a = -16
Solution
a = {0, -16}

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