0=-16x^2+24x+40

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Solution for 0=-16x^2+24x+40 equation:


Simplifying
0 = -16x2 + 24x + 40

Reorder the terms:
0 = 40 + 24x + -16x2

Solving
0 = 40 + 24x + -16x2

Solving for variable 'x'.

Combine like terms: 0 + -40 = -40
-40 + -24x + 16x2 = 40 + 24x + -16x2 + -40 + -24x + 16x2

Reorder the terms:
-40 + -24x + 16x2 = 40 + -40 + 24x + -24x + -16x2 + 16x2

Combine like terms: 40 + -40 = 0
-40 + -24x + 16x2 = 0 + 24x + -24x + -16x2 + 16x2
-40 + -24x + 16x2 = 24x + -24x + -16x2 + 16x2

Combine like terms: 24x + -24x = 0
-40 + -24x + 16x2 = 0 + -16x2 + 16x2
-40 + -24x + 16x2 = -16x2 + 16x2

Combine like terms: -16x2 + 16x2 = 0
-40 + -24x + 16x2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(-5 + -3x + 2x2) = 0

Factor a trinomial.
8((-1 + -1x)(5 + -2x)) = 0

Ignore the factor 8.

Subproblem 1

Set the factor '(-1 + -1x)' equal to zero and attempt to solve: Simplifying -1 + -1x = 0 Solving -1 + -1x = 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 + -1x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1x = 0 + 1 -1x = 0 + 1 Combine like terms: 0 + 1 = 1 -1x = 1 Divide each side by '-1'. x = -1 Simplifying x = -1

Subproblem 2

Set the factor '(5 + -2x)' equal to zero and attempt to solve: Simplifying 5 + -2x = 0 Solving 5 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -2x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2x = 0 + -5 -2x = 0 + -5 Combine like terms: 0 + -5 = -5 -2x = -5 Divide each side by '-2'. x = 2.5 Simplifying x = 2.5

Solution

x = {-1, 2.5}

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