7(a+6)=10[a-(5-a)]

Solution for 7(a+6)=10[a-(5-a)] equation:

Simplifying
7(a + 6) = 10[a + -1(5 + -1a)]

Reorder the terms:
7(6 + a) = 10[a + -1(5 + -1a)]
(6 * 7 + a * 7) = 10[a + -1(5 + -1a)]
(42 + 7a) = 10[a + -1(5 + -1a)]
42 + 7a = 10[a + (5 * -1 + -1a * -1)]
42 + 7a = 10[a + (-5 + 1a)]

Reorder the terms:
42 + 7a = 10[-5 + a + 1a]

Combine like terms: a + 1a = 2a
42 + 7a = 10[-5 + 2a]
42 + 7a = [-5 * 10 + 2a * 10]
42 + 7a = [-50 + 20a]

Solving
42 + 7a = -50 + 20a

Solving for variable 'a'.

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

Add '-20a' to each side of the equation.
42 + 7a + -20a = -50 + 20a + -20a

Combine like terms: 7a + -20a = -13a
42 + -13a = -50 + 20a + -20a

Combine like terms: 20a + -20a = 0
42 + -13a = -50 + 0
42 + -13a = -50

Add '-42' to each side of the equation.
42 + -42 + -13a = -50 + -42

Combine like terms: 42 + -42 = 0
0 + -13a = -50 + -42
-13a = -50 + -42

Combine like terms: -50 + -42 = -92
-13a = -92

Divide each side by '-13'.
a = 7.076923077

Simplifying
a = 7.076923077