10r^2+75r+140=0

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Solution for 10r^2+75r+140=0 equation:


Simplifying
10r2 + 75r + 140 = 0

Reorder the terms:
140 + 75r + 10r2 = 0

Solving
140 + 75r + 10r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '5'.
5(28 + 15r + 2r2) = 0

Factor a trinomial.
5((4 + r)(7 + 2r)) = 0

Ignore the factor 5.

Subproblem 1

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

Subproblem 2

Set the factor '(7 + 2r)' equal to zero and attempt to solve: Simplifying 7 + 2r = 0 Solving 7 + 2r = 0 Move all terms containing r to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + 2r = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 2r = 0 + -7 2r = 0 + -7 Combine like terms: 0 + -7 = -7 2r = -7 Divide each side by '2'. r = -3.5 Simplifying r = -3.5

Solution

r = {-4, -3.5}

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