100*0.75+100*0.25*(1+x)=100*(1+0.15)*0.90+100*(1+0.15)*0.10*(1+x)

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Solution for 100*0.75+100*0.25*(1+x)=100*(1+0.15)*0.90+100*(1+0.15)*0.10*(1+x) equation: 


Simplifying
100 * 0.75 + 100 * 0.25(1 + x) = 100(1 + 0.15) * 0.90 + 100(1 + 0.15) * 0.10(1 + x)

Multiply 100 * 0.75
75 + 100 * 0.25(1 + x) = 100(1 + 0.15) * 0.90 + 100(1 + 0.15) * 0.10(1 + x)

Multiply 100 * 0.25
75 + 25(1 + x) = 100(1 + 0.15) * 0.90 + 100(1 + 0.15) * 0.10(1 + x)
75 + (1 * 25 + x * 25) = 100(1 + 0.15) * 0.90 + 100(1 + 0.15) * 0.10(1 + x)
75 + (25 + 25x) = 100(1 + 0.15) * 0.90 + 100(1 + 0.15) * 0.10(1 + x)

Combine like terms: 75 + 25 = 100
100 + 25x = 100(1 + 0.15) * 0.90 + 100(1 + 0.15) * 0.10(1 + x)

Combine like terms: 1 + 0.15 = 1.15
100 + 25x = 100(1.15) * 0.90 + 100(1 + 0.15) * 0.10(1 + x)

Multiply 100 * 1.15
100 + 25x = 115 * 0.90 + 100(1 + 0.15) * 0.10(1 + x)

Multiply 115 * 0.90
100 + 25x = 103.5 + 100(1 + 0.15) * 0.10(1 + x)

Combine like terms: 1 + 0.15 = 1.15
100 + 25x = 103.5 + 100(1.15) * 0.10(1 + x)

Multiply 100 * 1.15
100 + 25x = 103.5 + 115 * 0.10(1 + x)

Multiply 115 * 0.10
100 + 25x = 103.5 + 11.5(1 + x)
100 + 25x = 103.5 + (1 * 11.5 + x * 11.5)
100 + 25x = 103.5 + (11.5 + 11.5x)

Combine like terms: 103.5 + 11.5 = 115
100 + 25x = 115 + 11.5x

Solving
100 + 25x = 115 + 11.5x

Solving for variable 'x'.

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

Add '-11.5x' to each side of the equation.
100 + 25x + -11.5x = 115 + 11.5x + -11.5x

Combine like terms: 25x + -11.5x = 13.5x
100 + 13.5x = 115 + 11.5x + -11.5x

Combine like terms: 11.5x + -11.5x = 0.0
100 + 13.5x = 115 + 0.0
100 + 13.5x = 115

Add '-100' to each side of the equation.
100 + -100 + 13.5x = 115 + -100

Combine like terms: 100 + -100 = 0
0 + 13.5x = 115 + -100
13.5x = 115 + -100

Combine like terms: 115 + -100 = 15
13.5x = 15

Divide each side by '13.5'.
x = 1.111111111

Simplifying
x = 1.111111111

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