(4x+32)(2x+1)=

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Solution for (4x+32)(2x+1)= equation:


Simplifying
(4x + 32)(2x + 1) = 0

Reorder the terms:
(32 + 4x)(2x + 1) = 0

Reorder the terms:
(32 + 4x)(1 + 2x) = 0

Multiply (32 + 4x) * (1 + 2x)
(32(1 + 2x) + 4x * (1 + 2x)) = 0
((1 * 32 + 2x * 32) + 4x * (1 + 2x)) = 0
((32 + 64x) + 4x * (1 + 2x)) = 0
(32 + 64x + (1 * 4x + 2x * 4x)) = 0
(32 + 64x + (4x + 8x2)) = 0

Combine like terms: 64x + 4x = 68x
(32 + 68x + 8x2) = 0

Solving
32 + 68x + 8x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(8 + 17x + 2x2) = 0

Factor a trinomial.
4((8 + x)(1 + 2x)) = 0

Ignore the factor 4.

Subproblem 1

Set the factor '(8 + x)' equal to zero and attempt to solve: Simplifying 8 + x = 0 Solving 8 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + x = 0 + -8 x = 0 + -8 Combine like terms: 0 + -8 = -8 x = -8 Simplifying x = -8

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 = {-8, -0.5}

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