100*0.6+100*0.4*(1+x)=100*(1+0.3)*0.90+100*(1+0.3)*0.10*(1+x)

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Solution for 100*0.6+100*0.4*(1+x)=100*(1+0.3)*0.90+100*(1+0.3)*0.10*(1+x) equation: 


Simplifying
100 * 0.6 + 100 * 0.4(1 + x) = 100(1 + 0.3) * 0.90 + 100(1 + 0.3) * 0.10(1 + x)

Multiply 100 * 0.6
60 + 100 * 0.4(1 + x) = 100(1 + 0.3) * 0.90 + 100(1 + 0.3) * 0.10(1 + x)

Multiply 100 * 0.4
60 + 40(1 + x) = 100(1 + 0.3) * 0.90 + 100(1 + 0.3) * 0.10(1 + x)
60 + (1 * 40 + x * 40) = 100(1 + 0.3) * 0.90 + 100(1 + 0.3) * 0.10(1 + x)
60 + (40 + 40x) = 100(1 + 0.3) * 0.90 + 100(1 + 0.3) * 0.10(1 + x)

Combine like terms: 60 + 40 = 100
100 + 40x = 100(1 + 0.3) * 0.90 + 100(1 + 0.3) * 0.10(1 + x)

Combine like terms: 1 + 0.3 = 1.3
100 + 40x = 100(1.3) * 0.90 + 100(1 + 0.3) * 0.10(1 + x)

Multiply 100 * 1.3
100 + 40x = 130 * 0.90 + 100(1 + 0.3) * 0.10(1 + x)

Multiply 130 * 0.90
100 + 40x = 117 + 100(1 + 0.3) * 0.10(1 + x)

Combine like terms: 1 + 0.3 = 1.3
100 + 40x = 117 + 100(1.3) * 0.10(1 + x)

Multiply 100 * 1.3
100 + 40x = 117 + 130 * 0.10(1 + x)

Multiply 130 * 0.10
100 + 40x = 117 + 13(1 + x)
100 + 40x = 117 + (1 * 13 + x * 13)
100 + 40x = 117 + (13 + 13x)

Combine like terms: 117 + 13 = 130
100 + 40x = 130 + 13x

Solving
100 + 40x = 130 + 13x

Solving for variable 'x'.

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

Add '-13x' to each side of the equation.
100 + 40x + -13x = 130 + 13x + -13x

Combine like terms: 40x + -13x = 27x
100 + 27x = 130 + 13x + -13x

Combine like terms: 13x + -13x = 0
100 + 27x = 130 + 0
100 + 27x = 130

Add '-100' to each side of the equation.
100 + -100 + 27x = 130 + -100

Combine like terms: 100 + -100 = 0
0 + 27x = 130 + -100
27x = 130 + -100

Combine like terms: 130 + -100 = 30
27x = 30

Divide each side by '27'.
x = 1.111111111

Simplifying
x = 1.111111111

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