(2n+5)(3n-4)=(n+2)(6n-7)

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Solution for (2n+5)(3n-4)=(n+2)(6n-7) equation: 


Simplifying
(2n + 5)(3n + -4) = (n + 2)(6n + -7)

Reorder the terms:
(5 + 2n)(3n + -4) = (n + 2)(6n + -7)

Reorder the terms:
(5 + 2n)(-4 + 3n) = (n + 2)(6n + -7)

Multiply (5 + 2n) * (-4 + 3n)
(5(-4 + 3n) + 2n * (-4 + 3n)) = (n + 2)(6n + -7)
((-4 * 5 + 3n * 5) + 2n * (-4 + 3n)) = (n + 2)(6n + -7)
((-20 + 15n) + 2n * (-4 + 3n)) = (n + 2)(6n + -7)
(-20 + 15n + (-4 * 2n + 3n * 2n)) = (n + 2)(6n + -7)
(-20 + 15n + (-8n + 6n2)) = (n + 2)(6n + -7)

Combine like terms: 15n + -8n = 7n
(-20 + 7n + 6n2) = (n + 2)(6n + -7)

Reorder the terms:
-20 + 7n + 6n2 = (2 + n)(6n + -7)

Reorder the terms:
-20 + 7n + 6n2 = (2 + n)(-7 + 6n)

Multiply (2 + n) * (-7 + 6n)
-20 + 7n + 6n2 = (2(-7 + 6n) + n(-7 + 6n))
-20 + 7n + 6n2 = ((-7 * 2 + 6n * 2) + n(-7 + 6n))
-20 + 7n + 6n2 = ((-14 + 12n) + n(-7 + 6n))
-20 + 7n + 6n2 = (-14 + 12n + (-7 * n + 6n * n))
-20 + 7n + 6n2 = (-14 + 12n + (-7n + 6n2))

Combine like terms: 12n + -7n = 5n
-20 + 7n + 6n2 = (-14 + 5n + 6n2)

Add '-6n2' to each side of the equation.
-20 + 7n + 6n2 + -6n2 = -14 + 5n + 6n2 + -6n2

Combine like terms: 6n2 + -6n2 = 0
-20 + 7n + 0 = -14 + 5n + 6n2 + -6n2
-20 + 7n = -14 + 5n + 6n2 + -6n2

Combine like terms: 6n2 + -6n2 = 0
-20 + 7n = -14 + 5n + 0
-20 + 7n = -14 + 5n

Solving
-20 + 7n = -14 + 5n

Solving for variable 'n'.

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

Add '-5n' to each side of the equation.
-20 + 7n + -5n = -14 + 5n + -5n

Combine like terms: 7n + -5n = 2n
-20 + 2n = -14 + 5n + -5n

Combine like terms: 5n + -5n = 0
-20 + 2n = -14 + 0
-20 + 2n = -14

Add '20' to each side of the equation.
-20 + 20 + 2n = -14 + 20

Combine like terms: -20 + 20 = 0
0 + 2n = -14 + 20
2n = -14 + 20

Combine like terms: -14 + 20 = 6
2n = 6

Divide each side by '2'.
n = 3

Simplifying
n = 3

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