(5r+4)(r-10)=-(21r-210)

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Solution for (5r+4)(r-10)=-(21r-210) equation: 


Simplifying
(5r + 4)(r + -10) = -1(21r + -210)

Reorder the terms:
(4 + 5r)(r + -10) = -1(21r + -210)

Reorder the terms:
(4 + 5r)(-10 + r) = -1(21r + -210)

Multiply (4 + 5r) * (-10 + r)
(4(-10 + r) + 5r * (-10 + r)) = -1(21r + -210)
((-10 * 4 + r * 4) + 5r * (-10 + r)) = -1(21r + -210)
((-40 + 4r) + 5r * (-10 + r)) = -1(21r + -210)
(-40 + 4r + (-10 * 5r + r * 5r)) = -1(21r + -210)
(-40 + 4r + (-50r + 5r2)) = -1(21r + -210)

Combine like terms: 4r + -50r = -46r
(-40 + -46r + 5r2) = -1(21r + -210)

Reorder the terms:
-40 + -46r + 5r2 = -1(-210 + 21r)
-40 + -46r + 5r2 = (-210 * -1 + 21r * -1)
-40 + -46r + 5r2 = (210 + -21r)

Solving
-40 + -46r + 5r2 = 210 + -21r

Solving for variable 'r'.

Reorder the terms:
-40 + -210 + -46r + 21r + 5r2 = 210 + -21r + -210 + 21r

Combine like terms: -40 + -210 = -250
-250 + -46r + 21r + 5r2 = 210 + -21r + -210 + 21r

Combine like terms: -46r + 21r = -25r
-250 + -25r + 5r2 = 210 + -21r + -210 + 21r

Reorder the terms:
-250 + -25r + 5r2 = 210 + -210 + -21r + 21r

Combine like terms: 210 + -210 = 0
-250 + -25r + 5r2 = 0 + -21r + 21r
-250 + -25r + 5r2 = -21r + 21r

Combine like terms: -21r + 21r = 0
-250 + -25r + 5r2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-50 + -5r + r2) = 0

Factor a trinomial.
5((-5 + -1r)(10 + -1r)) = 0

Ignore the factor 5.

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

Simplifying
-5 + -1r = 0

Solving
-5 + -1r = 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 + -1r = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1r = 0 + 5
-1r = 0 + 5

Combine like terms: 0 + 5 = 5
-1r = 5

Divide each side by '-1'.
r = -5

Simplifying
r = -5

Subproblem 2
Set the factor '(10 + -1r)' equal to zero and attempt to solve:

Simplifying
10 + -1r = 0

Solving
10 + -1r = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1r = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1r = 0 + -10
-1r = 0 + -10

Combine like terms: 0 + -10 = -10
-1r = -10

Divide each side by '-1'.
r = 10

Simplifying
r = 10
Solution
r = {-5, 10}

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