0=(4x-38)(4x+14)

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Solution for 0=(4x-38)(4x+14) equation: 


Simplifying
0 = (4x + -38)(4x + 14)

Reorder the terms:
0 = (-38 + 4x)(4x + 14)

Reorder the terms:
0 = (-38 + 4x)(14 + 4x)

Multiply (-38 + 4x) * (14 + 4x)
0 = (-38(14 + 4x) + 4x * (14 + 4x))
0 = ((14 * -38 + 4x * -38) + 4x * (14 + 4x))
0 = ((-532 + -152x) + 4x * (14 + 4x))
0 = (-532 + -152x + (14 * 4x + 4x * 4x))
0 = (-532 + -152x + (56x + 16x2))

Combine like terms: -152x + 56x = -96x
0 = (-532 + -96x + 16x2)

Solving
0 = -532 + -96x + 16x2

Solving for variable 'x'.

Combine like terms: 0 + 532 = 532
532 + 96x + -16x2 = -532 + -96x + 16x2 + 532 + 96x + -16x2

Reorder the terms:
532 + 96x + -16x2 = -532 + 532 + -96x + 96x + 16x2 + -16x2

Combine like terms: -532 + 532 = 0
532 + 96x + -16x2 = 0 + -96x + 96x + 16x2 + -16x2
532 + 96x + -16x2 = -96x + 96x + 16x2 + -16x2

Combine like terms: -96x + 96x = 0
532 + 96x + -16x2 = 0 + 16x2 + -16x2
532 + 96x + -16x2 = 16x2 + -16x2

Combine like terms: 16x2 + -16x2 = 0
532 + 96x + -16x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(133 + 24x + -4x2) = 0

Factor a trinomial.
4((19 + -2x)(7 + 2x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(19 + -2x)' equal to zero and attempt to solve:

Simplifying
19 + -2x = 0

Solving
19 + -2x = 0

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

Add '-19' to each side of the equation.
19 + -19 + -2x = 0 + -19

Combine like terms: 19 + -19 = 0
0 + -2x = 0 + -19
-2x = 0 + -19

Combine like terms: 0 + -19 = -19
-2x = -19

Divide each side by '-2'.
x = 9.5

Simplifying
x = 9.5

Subproblem 2
Set the factor '(7 + 2x)' equal to zero and attempt to solve:

Simplifying
7 + 2x = 0

Solving
7 + 2x = 0

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

Add '-7' to each side of the equation.
7 + -7 + 2x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 2x = 0 + -7
2x = 0 + -7

Combine like terms: 0 + -7 = -7
2x = -7

Divide each side by '2'.
x = -3.5

Simplifying
x = -3.5
Solution
x = {9.5, -3.5}

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