(2x+32)(2x+24)-560=0

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Solution for (2x+32)(2x+24)-560=0 equation: 


Simplifying
(2x + 32)(2x + 24) + -560 = 0

Reorder the terms:
(32 + 2x)(2x + 24) + -560 = 0

Reorder the terms:
(32 + 2x)(24 + 2x) + -560 = 0

Multiply (32 + 2x) * (24 + 2x)
(32(24 + 2x) + 2x * (24 + 2x)) + -560 = 0
((24 * 32 + 2x * 32) + 2x * (24 + 2x)) + -560 = 0
((768 + 64x) + 2x * (24 + 2x)) + -560 = 0
(768 + 64x + (24 * 2x + 2x * 2x)) + -560 = 0
(768 + 64x + (48x + 4x2)) + -560 = 0

Combine like terms: 64x + 48x = 112x
(768 + 112x + 4x2) + -560 = 0

Reorder the terms:
768 + -560 + 112x + 4x2 = 0

Combine like terms: 768 + -560 = 208
208 + 112x + 4x2 = 0

Solving
208 + 112x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(52 + 28x + x2) = 0

Factor a trinomial.
4((26 + x)(2 + x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(26 + x)' equal to zero and attempt to solve:

Simplifying
26 + x = 0

Solving
26 + x = 0

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

Add '-26' to each side of the equation.
26 + -26 + x = 0 + -26

Combine like terms: 26 + -26 = 0
0 + x = 0 + -26
x = 0 + -26

Combine like terms: 0 + -26 = -26
x = -26

Simplifying
x = -26

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

Simplifying
2 + x = 0

Solving
2 + x = 0

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

Add '-2' to each side of the equation.
2 + -2 + x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + x = 0 + -2
x = 0 + -2

Combine like terms: 0 + -2 = -2
x = -2

Simplifying
x = -2
Solution
x = {-26, -2}

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