2(5x-1)-7=3x(x-1)+5-4x

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Solution for 2(5x-1)-7=3x(x-1)+5-4x equation: 


Simplifying
2(5x + -1) + -7 = 3x(x + -1) + 5 + -4x

Reorder the terms:
2(-1 + 5x) + -7 = 3x(x + -1) + 5 + -4x
(-1 * 2 + 5x * 2) + -7 = 3x(x + -1) + 5 + -4x
(-2 + 10x) + -7 = 3x(x + -1) + 5 + -4x

Reorder the terms:
-2 + -7 + 10x = 3x(x + -1) + 5 + -4x

Combine like terms: -2 + -7 = -9
-9 + 10x = 3x(x + -1) + 5 + -4x

Reorder the terms:
-9 + 10x = 3x(-1 + x) + 5 + -4x
-9 + 10x = (-1 * 3x + x * 3x) + 5 + -4x
-9 + 10x = (-3x + 3x2) + 5 + -4x

Reorder the terms:
-9 + 10x = 5 + -3x + -4x + 3x2

Combine like terms: -3x + -4x = -7x
-9 + 10x = 5 + -7x + 3x2

Solving
-9 + 10x = 5 + -7x + 3x2

Solving for variable 'x'.

Reorder the terms:
-9 + -5 + 10x + 7x + -3x2 = 5 + -7x + 3x2 + -5 + 7x + -3x2

Combine like terms: -9 + -5 = -14
-14 + 10x + 7x + -3x2 = 5 + -7x + 3x2 + -5 + 7x + -3x2

Combine like terms: 10x + 7x = 17x
-14 + 17x + -3x2 = 5 + -7x + 3x2 + -5 + 7x + -3x2

Reorder the terms:
-14 + 17x + -3x2 = 5 + -5 + -7x + 7x + 3x2 + -3x2

Combine like terms: 5 + -5 = 0
-14 + 17x + -3x2 = 0 + -7x + 7x + 3x2 + -3x2
-14 + 17x + -3x2 = -7x + 7x + 3x2 + -3x2

Combine like terms: -7x + 7x = 0
-14 + 17x + -3x2 = 0 + 3x2 + -3x2
-14 + 17x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
-14 + 17x + -3x2 = 0

Factor a trinomial.
(-14 + 3x)(1 + -1x) = 0


Subproblem 1
Set the factor '(-14 + 3x)' equal to zero and attempt to solve:

Simplifying
-14 + 3x = 0

Solving
-14 + 3x = 0

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

Add '14' to each side of the equation.
-14 + 14 + 3x = 0 + 14

Combine like terms: -14 + 14 = 0
0 + 3x = 0 + 14
3x = 0 + 14

Combine like terms: 0 + 14 = 14
3x = 14

Divide each side by '3'.
x = 4.666666667

Simplifying
x = 4.666666667

Subproblem 2
Set the factor '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

Add '-1' to each side of the equation.
1 + -1 + -1x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1x = 0 + -1
-1x = 0 + -1

Combine like terms: 0 + -1 = -1
-1x = -1

Divide each side by '-1'.
x = 1

Simplifying
x = 1
Solution
x = {4.666666667, 1}

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