2(b-5)+3(b-2)=7(b-4)

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


Simplifying
2(b + -5) + 3(b + -2) = 7(b + -4)

Reorder the terms:
2(-5 + b) + 3(b + -2) = 7(b + -4)
(-5 * 2 + b * 2) + 3(b + -2) = 7(b + -4)
(-10 + 2b) + 3(b + -2) = 7(b + -4)

Reorder the terms:
-10 + 2b + 3(-2 + b) = 7(b + -4)
-10 + 2b + (-2 * 3 + b * 3) = 7(b + -4)
-10 + 2b + (-6 + 3b) = 7(b + -4)

Reorder the terms:
-10 + -6 + 2b + 3b = 7(b + -4)

Combine like terms: -10 + -6 = -16
-16 + 2b + 3b = 7(b + -4)

Combine like terms: 2b + 3b = 5b
-16 + 5b = 7(b + -4)

Reorder the terms:
-16 + 5b = 7(-4 + b)
-16 + 5b = (-4 * 7 + b * 7)
-16 + 5b = (-28 + 7b)

Solving
-16 + 5b = -28 + 7b

Solving for variable 'b'.

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

Add '-7b' to each side of the equation.
-16 + 5b + -7b = -28 + 7b + -7b

Combine like terms: 5b + -7b = -2b
-16 + -2b = -28 + 7b + -7b

Combine like terms: 7b + -7b = 0
-16 + -2b = -28 + 0
-16 + -2b = -28

Add '16' to each side of the equation.
-16 + 16 + -2b = -28 + 16

Combine like terms: -16 + 16 = 0
0 + -2b = -28 + 16
-2b = -28 + 16

Combine like terms: -28 + 16 = -12
-2b = -12

Divide each side by '-2'.
b = 6

Simplifying
b = 6

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