0=-16x^2-12x+40

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Solution for 0=-16x^2-12x+40 equation:


Simplifying
0 = -16x2 + -12x + 40

Reorder the terms:
0 = 40 + -12x + -16x2

Solving
0 = 40 + -12x + -16x2

Solving for variable 'x'.

Combine like terms: 0 + -40 = -40
-40 + 12x + 16x2 = 40 + -12x + -16x2 + -40 + 12x + 16x2

Reorder the terms:
-40 + 12x + 16x2 = 40 + -40 + -12x + 12x + -16x2 + 16x2

Combine like terms: 40 + -40 = 0
-40 + 12x + 16x2 = 0 + -12x + 12x + -16x2 + 16x2
-40 + 12x + 16x2 = -12x + 12x + -16x2 + 16x2

Combine like terms: -12x + 12x = 0
-40 + 12x + 16x2 = 0 + -16x2 + 16x2
-40 + 12x + 16x2 = -16x2 + 16x2

Combine like terms: -16x2 + 16x2 = 0
-40 + 12x + 16x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-10 + 3x + 4x2) = 0

Factor a trinomial.
4((-2 + -1x)(5 + -4x)) = 0

Ignore the factor 4.

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 '(5 + -4x)' equal to zero and attempt to solve: Simplifying 5 + -4x = 0 Solving 5 + -4x = 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 + -4x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -4x = 0 + -5 -4x = 0 + -5 Combine like terms: 0 + -5 = -5 -4x = -5 Divide each side by '-4'. x = 1.25 Simplifying x = 1.25

Solution

x = {-2, 1.25}

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