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

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


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

Reorder the terms:
x(-3 + x) = 4(x + 1) + 3x + -7x
(-3 * x + x * x) = 4(x + 1) + 3x + -7x
(-3x + x2) = 4(x + 1) + 3x + -7x

Reorder the terms:
-3x + x2 = 4(1 + x) + 3x + -7x
-3x + x2 = (1 * 4 + x * 4) + 3x + -7x
-3x + x2 = (4 + 4x) + 3x + -7x

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

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

Solving
-3x + x2 = 4

Solving for variable 'x'.

Reorder the terms:
-4 + -3x + x2 = 4 + -4

Combine like terms: 4 + -4 = 0
-4 + -3x + x2 = 0

Factor a trinomial.
(-1 + -1x)(4 + -1x) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {-1, 4}

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