-4(x+5)(x+5)-24=-600

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Solution for -4(x+5)(x+5)-24=-600 equation: 


Simplifying
-4(x + 5)(x + 5) + -24 = -600

Reorder the terms:
-4(5 + x)(x + 5) + -24 = -600

Reorder the terms:
-4(5 + x)(5 + x) + -24 = -600

Multiply (5 + x) * (5 + x)
-4(5(5 + x) + x(5 + x)) + -24 = -600
-4((5 * 5 + x * 5) + x(5 + x)) + -24 = -600
-4((25 + 5x) + x(5 + x)) + -24 = -600
-4(25 + 5x + (5 * x + x * x)) + -24 = -600
-4(25 + 5x + (5x + x2)) + -24 = -600

Combine like terms: 5x + 5x = 10x
-4(25 + 10x + x2) + -24 = -600
(25 * -4 + 10x * -4 + x2 * -4) + -24 = -600
(-100 + -40x + -4x2) + -24 = -600

Reorder the terms:
-100 + -24 + -40x + -4x2 = -600

Combine like terms: -100 + -24 = -124
-124 + -40x + -4x2 = -600

Solving
-124 + -40x + -4x2 = -600

Solving for variable 'x'.

Reorder the terms:
-124 + 600 + -40x + -4x2 = -600 + 600

Combine like terms: -124 + 600 = 476
476 + -40x + -4x2 = -600 + 600

Combine like terms: -600 + 600 = 0
476 + -40x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(119 + -10x + -1x2) = 0

Factor a trinomial.
4((7 + -1x)(17 + x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7

Subproblem 2
Set the factor '(17 + x)' equal to zero and attempt to solve:

Simplifying
17 + x = 0

Solving
17 + x = 0

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

Add '-17' to each side of the equation.
17 + -17 + x = 0 + -17

Combine like terms: 17 + -17 = 0
0 + x = 0 + -17
x = 0 + -17

Combine like terms: 0 + -17 = -17
x = -17

Simplifying
x = -17
Solution
x = {7, -17}

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