(5r-2)(7r-3)=

Solution for (5r-2)(7r-3)= equation:

Simplifying
(5r + -2)(7r + -3) = 0

Reorder the terms:
(-2 + 5r)(7r + -3) = 0

Reorder the terms:
(-2 + 5r)(-3 + 7r) = 0

Multiply (-2 + 5r) * (-3 + 7r)
(-2(-3 + 7r) + 5r * (-3 + 7r)) = 0
((-3 * -2 + 7r * -2) + 5r * (-3 + 7r)) = 0
((6 + -14r) + 5r * (-3 + 7r)) = 0
(6 + -14r + (-3 * 5r + 7r * 5r)) = 0
(6 + -14r + (-15r + 35r2)) = 0

Combine like terms: -14r + -15r = -29r
(6 + -29r + 35r2) = 0

Solving
6 + -29r + 35r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(2 + -5r)(3 + -7r) = 0

Subproblem 1
Set the factor '(2 + -5r)' equal to zero and attempt to solve:

Simplifying
2 + -5r = 0

Solving
2 + -5r = 0

Move all terms containing r to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + -2 + -5r = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -5r = 0 + -2
-5r = 0 + -2

Combine like terms: 0 + -2 = -2
-5r = -2

Divide each side by '-5'.
r = 0.4

Simplifying
r = 0.4
Subproblem 2
Set the factor '(3 + -7r)' equal to zero and attempt to solve:

Simplifying
3 + -7r = 0

Solving
3 + -7r = 0

Move all terms containing r to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + -3 + -7r = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -7r = 0 + -3
-7r = 0 + -3

Combine like terms: 0 + -3 = -3
-7r = -3

Divide each side by '-7'.
r = 0.4285714286

Simplifying
r = 0.4285714286
Solution
r = {0.4, 0.4285714286}