=(4r-5)(7r+2)

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Solution for =(4r-5)(7r+2) equation: 


Simplifying
0 = (4r + -5)(7r + 2)

Reorder the terms:
0 = (-5 + 4r)(7r + 2)

Reorder the terms:
0 = (-5 + 4r)(2 + 7r)

Multiply (-5 + 4r) * (2 + 7r)
0 = (-5(2 + 7r) + 4r * (2 + 7r))
0 = ((2 * -5 + 7r * -5) + 4r * (2 + 7r))
0 = ((-10 + -35r) + 4r * (2 + 7r))
0 = (-10 + -35r + (2 * 4r + 7r * 4r))
0 = (-10 + -35r + (8r + 28r2))

Combine like terms: -35r + 8r = -27r
0 = (-10 + -27r + 28r2)

Solving
0 = -10 + -27r + 28r2

Solving for variable 'r'.

Combine like terms: 0 + 10 = 10
10 + 27r + -28r2 = -10 + -27r + 28r2 + 10 + 27r + -28r2

Reorder the terms:
10 + 27r + -28r2 = -10 + 10 + -27r + 27r + 28r2 + -28r2

Combine like terms: -10 + 10 = 0
10 + 27r + -28r2 = 0 + -27r + 27r + 28r2 + -28r2
10 + 27r + -28r2 = -27r + 27r + 28r2 + -28r2

Combine like terms: -27r + 27r = 0
10 + 27r + -28r2 = 0 + 28r2 + -28r2
10 + 27r + -28r2 = 28r2 + -28r2

Combine like terms: 28r2 + -28r2 = 0
10 + 27r + -28r2 = 0

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


Subproblem 1
Set the factor '(5 + -4r)' equal to zero and attempt to solve:

Simplifying
5 + -4r = 0

Solving
5 + -4r = 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 + -4r = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -4r = 0 + -5
-4r = 0 + -5

Combine like terms: 0 + -5 = -5
-4r = -5

Divide each side by '-4'.
r = 1.25

Simplifying
r = 1.25

Subproblem 2
Set the factor '(2 + 7r)' equal to zero and attempt to solve:

Simplifying
2 + 7r = 0

Solving
2 + 7r = 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 + 7r = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 7r = 0 + -2
7r = 0 + -2

Combine like terms: 0 + -2 = -2
7r = -2

Divide each side by '7'.
r = -0.2857142857

Simplifying
r = -0.2857142857
Solution
r = {1.25, -0.2857142857}

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