(2x+32)(2x+29)=648

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Solution for (2x+32)(2x+29)=648 equation: 


Simplifying
(2x + 32)(2x + 29) = 648

Reorder the terms:
(32 + 2x)(2x + 29) = 648

Reorder the terms:
(32 + 2x)(29 + 2x) = 648

Multiply (32 + 2x) * (29 + 2x)
(32(29 + 2x) + 2x * (29 + 2x)) = 648
((29 * 32 + 2x * 32) + 2x * (29 + 2x)) = 648
((928 + 64x) + 2x * (29 + 2x)) = 648
(928 + 64x + (29 * 2x + 2x * 2x)) = 648
(928 + 64x + (58x + 4x2)) = 648

Combine like terms: 64x + 58x = 122x
(928 + 122x + 4x2) = 648

Solving
928 + 122x + 4x2 = 648

Solving for variable 'x'.

Reorder the terms:
928 + -648 + 122x + 4x2 = 648 + -648

Combine like terms: 928 + -648 = 280
280 + 122x + 4x2 = 648 + -648

Combine like terms: 648 + -648 = 0
280 + 122x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(140 + 61x + 2x2) = 0

Factor a trinomial.
2((28 + x)(5 + 2x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(28 + x)' equal to zero and attempt to solve:

Simplifying
28 + x = 0

Solving
28 + x = 0

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

Add '-28' to each side of the equation.
28 + -28 + x = 0 + -28

Combine like terms: 28 + -28 = 0
0 + x = 0 + -28
x = 0 + -28

Combine like terms: 0 + -28 = -28
x = -28

Simplifying
x = -28

Subproblem 2
Set the factor '(5 + 2x)' equal to zero and attempt to solve:

Simplifying
5 + 2x = 0

Solving
5 + 2x = 0

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

Add '-5' to each side of the equation.
5 + -5 + 2x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 2x = 0 + -5
2x = 0 + -5

Combine like terms: 0 + -5 = -5
2x = -5

Divide each side by '2'.
x = -2.5

Simplifying
x = -2.5
Solution
x = {-28, -2.5}

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