(x+1)(2-3x)+(3x-4)(x-1)=0

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Solution for (x+1)(2-3x)+(3x-4)(x-1)=0 equation: 


Simplifying
(x + 1)(2 + -3x) + (3x + -4)(x + -1) = 0

Reorder the terms:
(1 + x)(2 + -3x) + (3x + -4)(x + -1) = 0

Multiply (1 + x) * (2 + -3x)
(1(2 + -3x) + x(2 + -3x)) + (3x + -4)(x + -1) = 0
((2 * 1 + -3x * 1) + x(2 + -3x)) + (3x + -4)(x + -1) = 0
((2 + -3x) + x(2 + -3x)) + (3x + -4)(x + -1) = 0
(2 + -3x + (2 * x + -3x * x)) + (3x + -4)(x + -1) = 0
(2 + -3x + (2x + -3x2)) + (3x + -4)(x + -1) = 0

Combine like terms: -3x + 2x = -1x
(2 + -1x + -3x2) + (3x + -4)(x + -1) = 0

Reorder the terms:
2 + -1x + -3x2 + (-4 + 3x)(x + -1) = 0

Reorder the terms:
2 + -1x + -3x2 + (-4 + 3x)(-1 + x) = 0

Multiply (-4 + 3x) * (-1 + x)
2 + -1x + -3x2 + (-4(-1 + x) + 3x * (-1 + x)) = 0
2 + -1x + -3x2 + ((-1 * -4 + x * -4) + 3x * (-1 + x)) = 0
2 + -1x + -3x2 + ((4 + -4x) + 3x * (-1 + x)) = 0
2 + -1x + -3x2 + (4 + -4x + (-1 * 3x + x * 3x)) = 0
2 + -1x + -3x2 + (4 + -4x + (-3x + 3x2)) = 0

Combine like terms: -4x + -3x = -7x
2 + -1x + -3x2 + (4 + -7x + 3x2) = 0

Reorder the terms:
2 + 4 + -1x + -7x + -3x2 + 3x2 = 0

Combine like terms: 2 + 4 = 6
6 + -1x + -7x + -3x2 + 3x2 = 0

Combine like terms: -1x + -7x = -8x
6 + -8x + -3x2 + 3x2 = 0

Combine like terms: -3x2 + 3x2 = 0
6 + -8x + 0 = 0
6 + -8x = 0

Solving
6 + -8x = 0

Solving for variable 'x'.

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

Add '-6' to each side of the equation.
6 + -6 + -8x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -8x = 0 + -6
-8x = 0 + -6

Combine like terms: 0 + -6 = -6
-8x = -6

Divide each side by '-8'.
x = 0.75

Simplifying
x = 0.75

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