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

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

Simplifying
2a(a + 7) = 2(a + -3) * 2

Reorder the terms:
2a(7 + a) = 2(a + -3) * 2
(7 * 2a + a * 2a) = 2(a + -3) * 2
(14a + 2a2) = 2(a + -3) * 2

Reorder the terms:
14a + 2a2 = 2(-3 + a) * 2

Reorder the terms for easier multiplication:
14a + 2a2 = 2 * 2(-3 + a)

Multiply 2 * 2
14a + 2a2 = 4(-3 + a)
14a + 2a2 = (-3 * 4 + a * 4)
14a + 2a2 = (-12 + 4a)

Solving
14a + 2a2 = -12 + 4a

Solving for variable 'a'.

Reorder the terms:
12 + 14a + -4a + 2a2 = -12 + 4a + 12 + -4a

Combine like terms: 14a + -4a = 10a
12 + 10a + 2a2 = -12 + 4a + 12 + -4a

Reorder the terms:
12 + 10a + 2a2 = -12 + 12 + 4a + -4a

Combine like terms: -12 + 12 = 0
12 + 10a + 2a2 = 0 + 4a + -4a
12 + 10a + 2a2 = 4a + -4a

Combine like terms: 4a + -4a = 0
12 + 10a + 2a2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(6 + 5a + a2) = 0

Factor a trinomial.
2((3 + a)(2 + a)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(3 + a)' equal to zero and attempt to solve:

Simplifying
3 + a = 0

Solving
3 + a = 0

Move all terms containing a to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + -3 + a = 0 + -3

Combine like terms: 3 + -3 = 0
0 + a = 0 + -3
a = 0 + -3

Combine like terms: 0 + -3 = -3
a = -3

Simplifying
a = -3
Subproblem 2
Set the factor '(2 + a)' equal to zero and attempt to solve:

Simplifying
2 + a = 0

Solving
2 + a = 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 + a = 0 + -2

Combine like terms: 2 + -2 = 0
0 + a = 0 + -2
a = 0 + -2

Combine like terms: 0 + -2 = -2
a = -2

Simplifying
a = -2
Solution
a = {-3, -2}