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

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

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

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

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

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

Combine like terms: -12x + 3x = -9x
(-9 + -9x + 4x2) = -9(x + -3)

Reorder the terms:
-9 + -9x + 4x2 = -9(-3 + x)
-9 + -9x + 4x2 = (-3 * -9 + x * -9)
-9 + -9x + 4x2 = (27 + -9x)

Add '9x' to each side of the equation.
-9 + -9x + 9x + 4x2 = 27 + -9x + 9x

Combine like terms: -9x + 9x = 0
-9 + 0 + 4x2 = 27 + -9x + 9x
-9 + 4x2 = 27 + -9x + 9x

Combine like terms: -9x + 9x = 0
-9 + 4x2 = 27 + 0
-9 + 4x2 = 27

Solving
-9 + 4x2 = 27

Solving for variable 'x'.

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

Add '9' to each side of the equation.
-9 + 9 + 4x2 = 27 + 9

Combine like terms: -9 + 9 = 0
0 + 4x2 = 27 + 9
4x2 = 27 + 9

Combine like terms: 27 + 9 = 36
4x2 = 36

Divide each side by '4'.
x2 = 9

Simplifying
x2 = 9

Take the square root of each side:
x = {-3, 3}