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

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


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

Multiply x * x
(x2) + -7x + 7 = -3x + 4
x2 + -7x + 7 = -3x + 4

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

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

Solving
7 + -7x + x2 = 4 + -3x

Solving for variable 'x'.

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

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

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

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

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

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

Factor a trinomial.
(1 + -1x)(3 + -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 '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {1, 3}

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