(4a-3)(a+1)=a+33

Solution for (4a-3)(a+1)=a+33 equation:

Simplifying
(4a + -3)(a + 1) = a + 33

Reorder the terms:
(-3 + 4a)(a + 1) = a + 33

Reorder the terms:
(-3 + 4a)(1 + a) = a + 33

Multiply (-3 + 4a) * (1 + a)
(-3(1 + a) + 4a * (1 + a)) = a + 33
((1 * -3 + a * -3) + 4a * (1 + a)) = a + 33
((-3 + -3a) + 4a * (1 + a)) = a + 33
(-3 + -3a + (1 * 4a + a * 4a)) = a + 33
(-3 + -3a + (4a + 4a2)) = a + 33

Combine like terms: -3a + 4a = 1a
(-3 + 1a + 4a2) = a + 33

Reorder the terms:
-3 + 1a + 4a2 = 33 + a

Solving
-3 + 1a + 4a2 = 33 + a

Solving for variable 'a'.

Reorder the terms:
-3 + -33 + 1a + -1a + 4a2 = 33 + a + -33 + -1a

Combine like terms: -3 + -33 = -36
-36 + 1a + -1a + 4a2 = 33 + a + -33 + -1a

Combine like terms: 1a + -1a = 0
-36 + 0 + 4a2 = 33 + a + -33 + -1a
-36 + 4a2 = 33 + a + -33 + -1a

Reorder the terms:
-36 + 4a2 = 33 + -33 + a + -1a

Combine like terms: 33 + -33 = 0
-36 + 4a2 = 0 + a + -1a
-36 + 4a2 = a + -1a

Combine like terms: a + -1a = 0
-36 + 4a2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-9 + a2) = 0

Factor a difference between two squares.
4((3 + a)(-3 + a)) = 0

Ignore the factor 4.
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 '(-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
Solution
a = {-3, 3}