96=-16x^2+64x+32

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Solution for 96=-16x^2+64x+32 equation:


Simplifying
96 = -16x2 + 64x + 32

Reorder the terms:
96 = 32 + 64x + -16x2

Solving
96 = 32 + 64x + -16x2

Solving for variable 'x'.

Combine like terms: 96 + -32 = 64
64 + -64x + 16x2 = 32 + 64x + -16x2 + -32 + -64x + 16x2

Reorder the terms:
64 + -64x + 16x2 = 32 + -32 + 64x + -64x + -16x2 + 16x2

Combine like terms: 32 + -32 = 0
64 + -64x + 16x2 = 0 + 64x + -64x + -16x2 + 16x2
64 + -64x + 16x2 = 64x + -64x + -16x2 + 16x2

Combine like terms: 64x + -64x = 0
64 + -64x + 16x2 = 0 + -16x2 + 16x2
64 + -64x + 16x2 = -16x2 + 16x2

Combine like terms: -16x2 + 16x2 = 0
64 + -64x + 16x2 = 0

Factor out the Greatest Common Factor (GCF), '16'.
16(4 + -4x + x2) = 0

Factor a trinomial.
16((2 + -1x)(2 + -1x)) = 0

Ignore the factor 16.

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 '(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

Solution

x = {2, 2}

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