(2x+32)(2x-1)=0

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Solution for (2x+32)(2x-1)=0 equation: 


Simplifying
(2x + 32)(2x + -1) = 0

Reorder the terms:
(32 + 2x)(2x + -1) = 0

Reorder the terms:
(32 + 2x)(-1 + 2x) = 0

Multiply (32 + 2x) * (-1 + 2x)
(32(-1 + 2x) + 2x * (-1 + 2x)) = 0
((-1 * 32 + 2x * 32) + 2x * (-1 + 2x)) = 0
((-32 + 64x) + 2x * (-1 + 2x)) = 0
(-32 + 64x + (-1 * 2x + 2x * 2x)) = 0
(-32 + 64x + (-2x + 4x2)) = 0

Combine like terms: 64x + -2x = 62x
(-32 + 62x + 4x2) = 0

Solving
-32 + 62x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-16 + 31x + 2x2) = 0

Factor a trinomial.
2((-16 + -1x)(1 + -2x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-16 + -1x)' equal to zero and attempt to solve:

Simplifying
-16 + -1x = 0

Solving
-16 + -1x = 0

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

Add '16' to each side of the equation.
-16 + 16 + -1x = 0 + 16

Combine like terms: -16 + 16 = 0
0 + -1x = 0 + 16
-1x = 0 + 16

Combine like terms: 0 + 16 = 16
-1x = 16

Divide each side by '-1'.
x = -16

Simplifying
x = -16

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

Simplifying
1 + -2x = 0

Solving
1 + -2x = 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 + -2x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2x = 0 + -1
-2x = 0 + -1

Combine like terms: 0 + -1 = -1
-2x = -1

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5
Solution
x = {-16, 0.5}

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