0=-16x^2+92x+140

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Solution for 0=-16x^2+92x+140 equation:


Simplifying
0 = -16x2 + 92x + 140

Reorder the terms:
0 = 140 + 92x + -16x2

Solving
0 = 140 + 92x + -16x2

Solving for variable 'x'.

Combine like terms: 0 + -140 = -140
-140 + -92x + 16x2 = 140 + 92x + -16x2 + -140 + -92x + 16x2

Reorder the terms:
-140 + -92x + 16x2 = 140 + -140 + 92x + -92x + -16x2 + 16x2

Combine like terms: 140 + -140 = 0
-140 + -92x + 16x2 = 0 + 92x + -92x + -16x2 + 16x2
-140 + -92x + 16x2 = 92x + -92x + -16x2 + 16x2

Combine like terms: 92x + -92x = 0
-140 + -92x + 16x2 = 0 + -16x2 + 16x2
-140 + -92x + 16x2 = -16x2 + 16x2

Combine like terms: -16x2 + 16x2 = 0
-140 + -92x + 16x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-35 + -23x + 4x2) = 0

Factor a trinomial.
4((-5 + -4x)(7 + -1x)) = 0

Ignore the factor 4.

Subproblem 1

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

Subproblem 2

Set the factor '(7 + -1x)' equal to zero and attempt to solve: Simplifying 7 + -1x = 0 Solving 7 + -1x = 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 + -1x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1x = 0 + -7 -1x = 0 + -7 Combine like terms: 0 + -7 = -7 -1x = -7 Divide each side by '-1'. x = 7 Simplifying x = 7

Solution

x = {-1.25, 7}

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