(a+1)(2a+5)=(2a+3)(a-4)+5

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Solution for (a+1)(2a+5)=(2a+3)(a-4)+5 equation: 


Simplifying
(a + 1)(2a + 5) = (2a + 3)(a + -4) + 5

Reorder the terms:
(1 + a)(2a + 5) = (2a + 3)(a + -4) + 5

Reorder the terms:
(1 + a)(5 + 2a) = (2a + 3)(a + -4) + 5

Multiply (1 + a) * (5 + 2a)
(1(5 + 2a) + a(5 + 2a)) = (2a + 3)(a + -4) + 5
((5 * 1 + 2a * 1) + a(5 + 2a)) = (2a + 3)(a + -4) + 5
((5 + 2a) + a(5 + 2a)) = (2a + 3)(a + -4) + 5
(5 + 2a + (5 * a + 2a * a)) = (2a + 3)(a + -4) + 5
(5 + 2a + (5a + 2a2)) = (2a + 3)(a + -4) + 5

Combine like terms: 2a + 5a = 7a
(5 + 7a + 2a2) = (2a + 3)(a + -4) + 5

Reorder the terms:
5 + 7a + 2a2 = (3 + 2a)(a + -4) + 5

Reorder the terms:
5 + 7a + 2a2 = (3 + 2a)(-4 + a) + 5

Multiply (3 + 2a) * (-4 + a)
5 + 7a + 2a2 = (3(-4 + a) + 2a * (-4 + a)) + 5
5 + 7a + 2a2 = ((-4 * 3 + a * 3) + 2a * (-4 + a)) + 5
5 + 7a + 2a2 = ((-12 + 3a) + 2a * (-4 + a)) + 5
5 + 7a + 2a2 = (-12 + 3a + (-4 * 2a + a * 2a)) + 5
5 + 7a + 2a2 = (-12 + 3a + (-8a + 2a2)) + 5

Combine like terms: 3a + -8a = -5a
5 + 7a + 2a2 = (-12 + -5a + 2a2) + 5

Reorder the terms:
5 + 7a + 2a2 = -12 + 5 + -5a + 2a2

Combine like terms: -12 + 5 = -7
5 + 7a + 2a2 = -7 + -5a + 2a2

Add '-2a2' to each side of the equation.
5 + 7a + 2a2 + -2a2 = -7 + -5a + 2a2 + -2a2

Combine like terms: 2a2 + -2a2 = 0
5 + 7a + 0 = -7 + -5a + 2a2 + -2a2
5 + 7a = -7 + -5a + 2a2 + -2a2

Combine like terms: 2a2 + -2a2 = 0
5 + 7a = -7 + -5a + 0
5 + 7a = -7 + -5a

Solving
5 + 7a = -7 + -5a

Solving for variable 'a'.

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

Add '5a' to each side of the equation.
5 + 7a + 5a = -7 + -5a + 5a

Combine like terms: 7a + 5a = 12a
5 + 12a = -7 + -5a + 5a

Combine like terms: -5a + 5a = 0
5 + 12a = -7 + 0
5 + 12a = -7

Add '-5' to each side of the equation.
5 + -5 + 12a = -7 + -5

Combine like terms: 5 + -5 = 0
0 + 12a = -7 + -5
12a = -7 + -5

Combine like terms: -7 + -5 = -12
12a = -12

Divide each side by '12'.
a = -1

Simplifying
a = -1

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