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

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


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

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

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

Multiply (-4 + x) * (3 + x)
(-4(3 + x) + x(3 + x)) = 3x + -7
((3 * -4 + x * -4) + x(3 + x)) = 3x + -7
((-12 + -4x) + x(3 + x)) = 3x + -7
(-12 + -4x + (3 * x + x * x)) = 3x + -7
(-12 + -4x + (3x + x2)) = 3x + -7

Combine like terms: -4x + 3x = -1x
(-12 + -1x + x2) = 3x + -7

Reorder the terms:
-12 + -1x + x2 = -7 + 3x

Solving
-12 + -1x + x2 = -7 + 3x

Solving for variable 'x'.

Reorder the terms:
-12 + 7 + -1x + -3x + x2 = -7 + 3x + 7 + -3x

Combine like terms: -12 + 7 = -5
-5 + -1x + -3x + x2 = -7 + 3x + 7 + -3x

Combine like terms: -1x + -3x = -4x
-5 + -4x + x2 = -7 + 3x + 7 + -3x

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

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

Combine like terms: 3x + -3x = 0
-5 + -4x + x2 = 0

Factor a trinomial.
(-1 + -1x)(5 + -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 '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {-1, 5}

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