3(1-x)(5-9x)=2(15x^2+22x+7)-(3x^2+51x-71)

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Solution for 3(1-x)(5-9x)=2(15x^2+22x+7)-(3x^2+51x-71) equation:


Simplifying
3(1 + -1x)(5 + -9x) = 2(15x2 + 22x + 7) + -1(3x2 + 51x + -71)

Multiply (1 + -1x) * (5 + -9x)
3(1(5 + -9x) + -1x * (5 + -9x)) = 2(15x2 + 22x + 7) + -1(3x2 + 51x + -71)
3((5 * 1 + -9x * 1) + -1x * (5 + -9x)) = 2(15x2 + 22x + 7) + -1(3x2 + 51x + -71)
3((5 + -9x) + -1x * (5 + -9x)) = 2(15x2 + 22x + 7) + -1(3x2 + 51x + -71)
3(5 + -9x + (5 * -1x + -9x * -1x)) = 2(15x2 + 22x + 7) + -1(3x2 + 51x + -71)
3(5 + -9x + (-5x + 9x2)) = 2(15x2 + 22x + 7) + -1(3x2 + 51x + -71)

Combine like terms: -9x + -5x = -14x
3(5 + -14x + 9x2) = 2(15x2 + 22x + 7) + -1(3x2 + 51x + -71)
(5 * 3 + -14x * 3 + 9x2 * 3) = 2(15x2 + 22x + 7) + -1(3x2 + 51x + -71)
(15 + -42x + 27x2) = 2(15x2 + 22x + 7) + -1(3x2 + 51x + -71)

Reorder the terms:
15 + -42x + 27x2 = 2(7 + 22x + 15x2) + -1(3x2 + 51x + -71)
15 + -42x + 27x2 = (7 * 2 + 22x * 2 + 15x2 * 2) + -1(3x2 + 51x + -71)
15 + -42x + 27x2 = (14 + 44x + 30x2) + -1(3x2 + 51x + -71)

Reorder the terms:
15 + -42x + 27x2 = 14 + 44x + 30x2 + -1(-71 + 51x + 3x2)
15 + -42x + 27x2 = 14 + 44x + 30x2 + (-71 * -1 + 51x * -1 + 3x2 * -1)
15 + -42x + 27x2 = 14 + 44x + 30x2 + (71 + -51x + -3x2)

Reorder the terms:
15 + -42x + 27x2 = 14 + 71 + 44x + -51x + 30x2 + -3x2

Combine like terms: 14 + 71 = 85
15 + -42x + 27x2 = 85 + 44x + -51x + 30x2 + -3x2

Combine like terms: 44x + -51x = -7x
15 + -42x + 27x2 = 85 + -7x + 30x2 + -3x2

Combine like terms: 30x2 + -3x2 = 27x2
15 + -42x + 27x2 = 85 + -7x + 27x2

Add '-27x2' to each side of the equation.
15 + -42x + 27x2 + -27x2 = 85 + -7x + 27x2 + -27x2

Combine like terms: 27x2 + -27x2 = 0
15 + -42x + 0 = 85 + -7x + 27x2 + -27x2
15 + -42x = 85 + -7x + 27x2 + -27x2

Combine like terms: 27x2 + -27x2 = 0
15 + -42x = 85 + -7x + 0
15 + -42x = 85 + -7x

Solving
15 + -42x = 85 + -7x

Solving for variable 'x'.

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

Add '7x' to each side of the equation.
15 + -42x + 7x = 85 + -7x + 7x

Combine like terms: -42x + 7x = -35x
15 + -35x = 85 + -7x + 7x

Combine like terms: -7x + 7x = 0
15 + -35x = 85 + 0
15 + -35x = 85

Add '-15' to each side of the equation.
15 + -15 + -35x = 85 + -15

Combine like terms: 15 + -15 = 0
0 + -35x = 85 + -15
-35x = 85 + -15

Combine like terms: 85 + -15 = 70
-35x = 70

Divide each side by '-35'.
x = -2

Simplifying
x = -2

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