0=-16x^2+32x-7

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Solution for 0=-16x^2+32x-7 equation: 


Simplifying
0 = -16x2 + 32x + -7

Reorder the terms:
0 = -7 + 32x + -16x2

Solving
0 = -7 + 32x + -16x2

Solving for variable 'x'.

Combine like terms: 0 + 7 = 7
7 + -32x + 16x2 = -7 + 32x + -16x2 + 7 + -32x + 16x2

Reorder the terms:
7 + -32x + 16x2 = -7 + 7 + 32x + -32x + -16x2 + 16x2

Combine like terms: -7 + 7 = 0
7 + -32x + 16x2 = 0 + 32x + -32x + -16x2 + 16x2
7 + -32x + 16x2 = 32x + -32x + -16x2 + 16x2

Combine like terms: 32x + -32x = 0
7 + -32x + 16x2 = 0 + -16x2 + 16x2
7 + -32x + 16x2 = -16x2 + 16x2

Combine like terms: -16x2 + 16x2 = 0
7 + -32x + 16x2 = 0

Factor a trinomial.
(1 + -4x)(7 + -4x) = 0


Subproblem 1
Set the factor '(1 + -4x)' equal to zero and attempt to solve:

Simplifying
1 + -4x = 0

Solving
1 + -4x = 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 + -4x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -4x = 0 + -1
-4x = 0 + -1

Combine like terms: 0 + -1 = -1
-4x = -1

Divide each side by '-4'.
x = 0.25

Simplifying
x = 0.25

Subproblem 2
Set the factor '(7 + -4x)' equal to zero and attempt to solve:

Simplifying
7 + -4x = 0

Solving
7 + -4x = 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 + -4x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -4x = 0 + -7
-4x = 0 + -7

Combine like terms: 0 + -7 = -7
-4x = -7

Divide each side by '-4'.
x = 1.75

Simplifying
x = 1.75
Solution
x = {0.25, 1.75}

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