4q+1(1-q)=2q+10(1-q)

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Solution for 4q+1(1-q)=2q+10(1-q) equation:


Simplifying
4q + 1(1 + -1q) = 2q + 10(1 + -1q)
4q + (1 * 1 + -1q * 1) = 2q + 10(1 + -1q)
4q + (1 + -1q) = 2q + 10(1 + -1q)

Reorder the terms:
1 + 4q + -1q = 2q + 10(1 + -1q)

Combine like terms: 4q + -1q = 3q
1 + 3q = 2q + 10(1 + -1q)
1 + 3q = 2q + (1 * 10 + -1q * 10)
1 + 3q = 2q + (10 + -10q)

Reorder the terms:
1 + 3q = 10 + 2q + -10q

Combine like terms: 2q + -10q = -8q
1 + 3q = 10 + -8q

Solving
1 + 3q = 10 + -8q

Solving for variable 'q'.

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

Add '8q' to each side of the equation.
1 + 3q + 8q = 10 + -8q + 8q

Combine like terms: 3q + 8q = 11q
1 + 11q = 10 + -8q + 8q

Combine like terms: -8q + 8q = 0
1 + 11q = 10 + 0
1 + 11q = 10

Add '-1' to each side of the equation.
1 + -1 + 11q = 10 + -1

Combine like terms: 1 + -1 = 0
0 + 11q = 10 + -1
11q = 10 + -1

Combine like terms: 10 + -1 = 9
11q = 9

Divide each side by '11'.
q = 0.8181818182

Simplifying
q = 0.8181818182

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