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

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


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

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

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

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

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

Reorder the terms:
-12 + 1x + x2 = 4 + 7x

Solving
-12 + 1x + x2 = 4 + 7x

Solving for variable 'x'.

Reorder the terms:
-12 + -4 + 1x + -7x + x2 = 4 + 7x + -4 + -7x

Combine like terms: -12 + -4 = -16
-16 + 1x + -7x + x2 = 4 + 7x + -4 + -7x

Combine like terms: 1x + -7x = -6x
-16 + -6x + x2 = 4 + 7x + -4 + -7x

Reorder the terms:
-16 + -6x + x2 = 4 + -4 + 7x + -7x

Combine like terms: 4 + -4 = 0
-16 + -6x + x2 = 0 + 7x + -7x
-16 + -6x + x2 = 7x + -7x

Combine like terms: 7x + -7x = 0
-16 + -6x + x2 = 0

Factor a trinomial.
(-2 + -1x)(8 + -1x) = 0


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

Simplifying
-2 + -1x = 0

Solving
-2 + -1x = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1x = 0 + 2
-1x = 0 + 2

Combine like terms: 0 + 2 = 2
-1x = 2

Divide each side by '-1'.
x = -2

Simplifying
x = -2

Subproblem 2
Set the factor '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 0 + -8
-1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1x = -8

Divide each side by '-1'.
x = 8

Simplifying
x = 8
Solution
x = {-2, 8}

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