(3x-4)(x-1)+21-(x-1)(3x+5)=0

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Solution for (3x-4)(x-1)+21-(x-1)(3x+5)=0 equation: 


Simplifying
(3x + -4)(x + -1) + 21 + -1(x + -1)(3x + 5) = 0

Reorder the terms:
(-4 + 3x)(x + -1) + 21 + -1(x + -1)(3x + 5) = 0

Reorder the terms:
(-4 + 3x)(-1 + x) + 21 + -1(x + -1)(3x + 5) = 0

Multiply (-4 + 3x) * (-1 + x)
(-4(-1 + x) + 3x * (-1 + x)) + 21 + -1(x + -1)(3x + 5) = 0
((-1 * -4 + x * -4) + 3x * (-1 + x)) + 21 + -1(x + -1)(3x + 5) = 0
((4 + -4x) + 3x * (-1 + x)) + 21 + -1(x + -1)(3x + 5) = 0
(4 + -4x + (-1 * 3x + x * 3x)) + 21 + -1(x + -1)(3x + 5) = 0
(4 + -4x + (-3x + 3x2)) + 21 + -1(x + -1)(3x + 5) = 0

Combine like terms: -4x + -3x = -7x
(4 + -7x + 3x2) + 21 + -1(x + -1)(3x + 5) = 0

Reorder the terms:
4 + -7x + 3x2 + 21 + -1(-1 + x)(3x + 5) = 0

Reorder the terms:
4 + -7x + 3x2 + 21 + -1(-1 + x)(5 + 3x) = 0

Multiply (-1 + x) * (5 + 3x)
4 + -7x + 3x2 + 21 + -1(-1(5 + 3x) + x(5 + 3x)) = 0
4 + -7x + 3x2 + 21 + -1((5 * -1 + 3x * -1) + x(5 + 3x)) = 0
4 + -7x + 3x2 + 21 + -1((-5 + -3x) + x(5 + 3x)) = 0
4 + -7x + 3x2 + 21 + -1(-5 + -3x + (5 * x + 3x * x)) = 0
4 + -7x + 3x2 + 21 + -1(-5 + -3x + (5x + 3x2)) = 0

Combine like terms: -3x + 5x = 2x
4 + -7x + 3x2 + 21 + -1(-5 + 2x + 3x2) = 0
4 + -7x + 3x2 + 21 + (-5 * -1 + 2x * -1 + 3x2 * -1) = 0
4 + -7x + 3x2 + 21 + (5 + -2x + -3x2) = 0

Reorder the terms:
4 + 21 + 5 + -7x + -2x + 3x2 + -3x2 = 0

Combine like terms: 4 + 21 = 25
25 + 5 + -7x + -2x + 3x2 + -3x2 = 0

Combine like terms: 25 + 5 = 30
30 + -7x + -2x + 3x2 + -3x2 = 0

Combine like terms: -7x + -2x = -9x
30 + -9x + 3x2 + -3x2 = 0

Combine like terms: 3x2 + -3x2 = 0
30 + -9x + 0 = 0
30 + -9x = 0

Solving
30 + -9x = 0

Solving for variable 'x'.

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

Add '-30' to each side of the equation.
30 + -30 + -9x = 0 + -30

Combine like terms: 30 + -30 = 0
0 + -9x = 0 + -30
-9x = 0 + -30

Combine like terms: 0 + -30 = -30
-9x = -30

Divide each side by '-9'.
x = 3.333333333

Simplifying
x = 3.333333333

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