3(x+4)(x+4)-75=0

Solution for 3(x+4)(x+4)-75=0 equation:

Simplifying
3(x + 4)(x + 4) + -75 = 0

Reorder the terms:
3(4 + x)(x + 4) + -75 = 0

Reorder the terms:
3(4 + x)(4 + x) + -75 = 0

Multiply (4 + x) * (4 + x)
3(4(4 + x) + x(4 + x)) + -75 = 0
3((4 * 4 + x * 4) + x(4 + x)) + -75 = 0
3((16 + 4x) + x(4 + x)) + -75 = 0
3(16 + 4x + (4 * x + x * x)) + -75 = 0
3(16 + 4x + (4x + x2)) + -75 = 0

Combine like terms: 4x + 4x = 8x
3(16 + 8x + x2) + -75 = 0
(16 * 3 + 8x * 3 + x2 * 3) + -75 = 0
(48 + 24x + 3x2) + -75 = 0

Reorder the terms:
48 + -75 + 24x + 3x2 = 0

Combine like terms: 48 + -75 = -27
-27 + 24x + 3x2 = 0

Solving
-27 + 24x + 3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-9 + 8x + x2) = 0

Factor a trinomial.
3((-9 + -1x)(1 + -1x)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-9 + -1x)' equal to zero and attempt to solve:

Simplifying
-9 + -1x = 0

Solving
-9 + -1x = 0

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

Add '9' to each side of the equation.
-9 + 9 + -1x = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1x = 0 + 9
-1x = 0 + 9

Combine like terms: 0 + 9 = 9
-1x = 9

Divide each side by '-1'.
x = -9

Simplifying
x = -9
Subproblem 2
Set the factor '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

Add '-1' to each side of the equation.
1 + -1 + -1x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1x = 0 + -1
-1x = 0 + -1

Combine like terms: 0 + -1 = -1
-1x = -1

Divide each side by '-1'.
x = 1

Simplifying
x = 1
Solution
x = {-9, 1}