4x(32+16x)=2x+4

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Solution for 4x(32+16x)=2x+4 equation: 


Simplifying
4x(32 + 16x) = 2x + 4
(32 * 4x + 16x * 4x) = 2x + 4
(128x + 64x2) = 2x + 4

Reorder the terms:
128x + 64x2 = 4 + 2x

Solving
128x + 64x2 = 4 + 2x

Solving for variable 'x'.

Reorder the terms:
-4 + 128x + -2x + 64x2 = 4 + 2x + -4 + -2x

Combine like terms: 128x + -2x = 126x
-4 + 126x + 64x2 = 4 + 2x + -4 + -2x

Reorder the terms:
-4 + 126x + 64x2 = 4 + -4 + 2x + -2x

Combine like terms: 4 + -4 = 0
-4 + 126x + 64x2 = 0 + 2x + -2x
-4 + 126x + 64x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
-4 + 126x + 64x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-2 + 63x + 32x2) = 0

Factor a trinomial.
2((-2 + -1x)(1 + -32x)) = 0

Ignore the factor 2.

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

Simplifying
-2 + -1x = 0

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

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

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

Divide each side by '-1'.
x = -2

Simplifying
x = -2

Subproblem 2
Set the factor '(1 + -32x)' equal to zero and attempt to solve:

Simplifying
1 + -32x = 0

Solving
1 + -32x = 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 + -32x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -32x = 0 + -1
-32x = 0 + -1

Combine like terms: 0 + -1 = -1
-32x = -1

Divide each side by '-32'.
x = 0.03125

Simplifying
x = 0.03125
Solution
x = {-2, 0.03125}

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