(7r+4)(3r-5)=0

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Solution for (7r+4)(3r-5)=0 equation:


Simplifying
(7r + 4)(3r + -5) = 0

Reorder the terms:
(4 + 7r)(3r + -5) = 0

Reorder the terms:
(4 + 7r)(-5 + 3r) = 0

Multiply (4 + 7r) * (-5 + 3r)
(4(-5 + 3r) + 7r * (-5 + 3r)) = 0
((-5 * 4 + 3r * 4) + 7r * (-5 + 3r)) = 0
((-20 + 12r) + 7r * (-5 + 3r)) = 0
(-20 + 12r + (-5 * 7r + 3r * 7r)) = 0
(-20 + 12r + (-35r + 21r2)) = 0

Combine like terms: 12r + -35r = -23r
(-20 + -23r + 21r2) = 0

Solving
-20 + -23r + 21r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(-4 + -7r)(5 + -3r) = 0

Subproblem 1

Set the factor '(-4 + -7r)' equal to zero and attempt to solve: Simplifying -4 + -7r = 0 Solving -4 + -7r = 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 + -7r = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -7r = 0 + 4 -7r = 0 + 4 Combine like terms: 0 + 4 = 4 -7r = 4 Divide each side by '-7'. r = -0.5714285714 Simplifying r = -0.5714285714

Subproblem 2

Set the factor '(5 + -3r)' equal to zero and attempt to solve: Simplifying 5 + -3r = 0 Solving 5 + -3r = 0 Move all terms containing r to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -3r = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -3r = 0 + -5 -3r = 0 + -5 Combine like terms: 0 + -5 = -5 -3r = -5 Divide each side by '-3'. r = 1.666666667 Simplifying r = 1.666666667

Solution

r = {-0.5714285714, 1.666666667}

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