(x-3)(9x+3)=-24(x-3)

Solution for (x-3)(9x+3)=-24(x-3) equation:

Simplifying
(x + -3)(9x + 3) = -24(x + -3)

Reorder the terms:
(-3 + x)(9x + 3) = -24(x + -3)

Reorder the terms:
(-3 + x)(3 + 9x) = -24(x + -3)

Multiply (-3 + x) * (3 + 9x)
(-3(3 + 9x) + x(3 + 9x)) = -24(x + -3)
((3 * -3 + 9x * -3) + x(3 + 9x)) = -24(x + -3)
((-9 + -27x) + x(3 + 9x)) = -24(x + -3)
(-9 + -27x + (3 * x + 9x * x)) = -24(x + -3)
(-9 + -27x + (3x + 9x2)) = -24(x + -3)

Combine like terms: -27x + 3x = -24x
(-9 + -24x + 9x2) = -24(x + -3)

Reorder the terms:
-9 + -24x + 9x2 = -24(-3 + x)
-9 + -24x + 9x2 = (-3 * -24 + x * -24)
-9 + -24x + 9x2 = (72 + -24x)

Add '24x' to each side of the equation.
-9 + -24x + 24x + 9x2 = 72 + -24x + 24x

Combine like terms: -24x + 24x = 0
-9 + 0 + 9x2 = 72 + -24x + 24x
-9 + 9x2 = 72 + -24x + 24x

Combine like terms: -24x + 24x = 0
-9 + 9x2 = 72 + 0
-9 + 9x2 = 72

Solving
-9 + 9x2 = 72

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 + 9x2 = 72 + 9

Combine like terms: -9 + 9 = 0
0 + 9x2 = 72 + 9
9x2 = 72 + 9

Combine like terms: 72 + 9 = 81
9x2 = 81

Divide each side by '9'.
x2 = 9

Simplifying
x2 = 9

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