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

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


Simplifying
0 = -2x2 + 16x + -32

Reorder the terms:
0 = -32 + 16x + -2x2

Solving
0 = -32 + 16x + -2x2

Solving for variable 'x'.

Combine like terms: 0 + 32 = 32
32 + -16x + 2x2 = -32 + 16x + -2x2 + 32 + -16x + 2x2

Reorder the terms:
32 + -16x + 2x2 = -32 + 32 + 16x + -16x + -2x2 + 2x2

Combine like terms: -32 + 32 = 0
32 + -16x + 2x2 = 0 + 16x + -16x + -2x2 + 2x2
32 + -16x + 2x2 = 16x + -16x + -2x2 + 2x2

Combine like terms: 16x + -16x = 0
32 + -16x + 2x2 = 0 + -2x2 + 2x2
32 + -16x + 2x2 = -2x2 + 2x2

Combine like terms: -2x2 + 2x2 = 0
32 + -16x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(16 + -8x + x2) = 0

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

Ignore the factor 2.

Subproblem 1

Set the factor '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4

Subproblem 2

Set the factor '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4

Solution

x = {4, 4}

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