(4x-4)(x+3)=7x-9

Solution for (4x-4)(x+3)=7x-9 equation:

Simplifying
(4x + -4)(x + 3) = 7x + -9

Reorder the terms:
(-4 + 4x)(x + 3) = 7x + -9

Reorder the terms:
(-4 + 4x)(3 + x) = 7x + -9

Multiply (-4 + 4x) * (3 + x)
(-4(3 + x) + 4x * (3 + x)) = 7x + -9
((3 * -4 + x * -4) + 4x * (3 + x)) = 7x + -9
((-12 + -4x) + 4x * (3 + x)) = 7x + -9
(-12 + -4x + (3 * 4x + x * 4x)) = 7x + -9
(-12 + -4x + (12x + 4x2)) = 7x + -9

Combine like terms: -4x + 12x = 8x
(-12 + 8x + 4x2) = 7x + -9

Reorder the terms:
-12 + 8x + 4x2 = -9 + 7x

Solving
-12 + 8x + 4x2 = -9 + 7x

Solving for variable 'x'.

Reorder the terms:
-12 + 9 + 8x + -7x + 4x2 = -9 + 7x + 9 + -7x

Combine like terms: -12 + 9 = -3
-3 + 8x + -7x + 4x2 = -9 + 7x + 9 + -7x

Combine like terms: 8x + -7x = 1x
-3 + 1x + 4x2 = -9 + 7x + 9 + -7x

Reorder the terms:
-3 + 1x + 4x2 = -9 + 9 + 7x + -7x

Combine like terms: -9 + 9 = 0
-3 + 1x + 4x2 = 0 + 7x + -7x
-3 + 1x + 4x2 = 7x + -7x

Combine like terms: 7x + -7x = 0
-3 + 1x + 4x2 = 0

Factor a trinomial.
(-1 + -1x)(3 + -4x) = 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 + -4x)' equal to zero and attempt to solve:

Simplifying
3 + -4x = 0

Solving
3 + -4x = 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 + -4x = 0 + -3

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

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

Divide each side by '-4'.
x = 0.75

Simplifying
x = 0.75
Solution
x = {-1, 0.75}