r^2+7r=4r(4)(r+7)

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


Simplifying
r2 + 7r = 4r(4)(r + 7)

Reorder the terms:
7r + r2 = 4r(4)(r + 7)

Reorder the terms:
7r + r2 = 4r * 4(7 + r)

Reorder the terms for easier multiplication:
7r + r2 = 4 * 4r(7 + r)

Multiply 4 * 4
7r + r2 = 16r(7 + r)
7r + r2 = (7 * 16r + r * 16r)
7r + r2 = (112r + 16r2)

Solving
7r + r2 = 112r + 16r2

Solving for variable 'r'.

Reorder the terms:
7r + -112r + r2 + -16r2 = 112r + 16r2 + -112r + -16r2

Combine like terms: 7r + -112r = -105r
-105r + r2 + -16r2 = 112r + 16r2 + -112r + -16r2

Combine like terms: r2 + -16r2 = -15r2
-105r + -15r2 = 112r + 16r2 + -112r + -16r2

Reorder the terms:
-105r + -15r2 = 112r + -112r + 16r2 + -16r2

Combine like terms: 112r + -112r = 0
-105r + -15r2 = 0 + 16r2 + -16r2
-105r + -15r2 = 16r2 + -16r2

Combine like terms: 16r2 + -16r2 = 0
-105r + -15r2 = 0

Factor out the Greatest Common Factor (GCF), '-15r'.
-15r(7 + r) = 0

Ignore the factor -15.

Subproblem 1
Set the factor 'r' equal to zero and attempt to solve:

Simplifying
r = 0

Solving
r = 0

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

Simplifying
r = 0

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

Simplifying
7 + r = 0

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

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

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

Simplifying
r = -7
Solution
r = {0, -7}

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