(x-9)(x+9)=4(x-15)

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Solution for (x-9)(x+9)=4(x-15) equation: 


Simplifying
(x + -9)(x + 9) = 4(x + -15)

Reorder the terms:
(-9 + x)(x + 9) = 4(x + -15)

Reorder the terms:
(-9 + x)(9 + x) = 4(x + -15)

Multiply (-9 + x) * (9 + x)
(-9(9 + x) + x(9 + x)) = 4(x + -15)
((9 * -9 + x * -9) + x(9 + x)) = 4(x + -15)
((-81 + -9x) + x(9 + x)) = 4(x + -15)
(-81 + -9x + (9 * x + x * x)) = 4(x + -15)
(-81 + -9x + (9x + x2)) = 4(x + -15)

Combine like terms: -9x + 9x = 0
(-81 + 0 + x2) = 4(x + -15)
(-81 + x2) = 4(x + -15)

Reorder the terms:
-81 + x2 = 4(-15 + x)
-81 + x2 = (-15 * 4 + x * 4)
-81 + x2 = (-60 + 4x)

Solving
-81 + x2 = -60 + 4x

Solving for variable 'x'.

Reorder the terms:
-81 + 60 + -4x + x2 = -60 + 4x + 60 + -4x

Combine like terms: -81 + 60 = -21
-21 + -4x + x2 = -60 + 4x + 60 + -4x

Reorder the terms:
-21 + -4x + x2 = -60 + 60 + 4x + -4x

Combine like terms: -60 + 60 = 0
-21 + -4x + x2 = 0 + 4x + -4x
-21 + -4x + x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
-21 + -4x + x2 = 0

Factor a trinomial.
(-3 + -1x)(7 + -1x) = 0


Subproblem 1
Set the factor '(-3 + -1x)' equal to zero and attempt to solve:

Simplifying
-3 + -1x = 0

Solving
-3 + -1x = 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 + -1x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1x = 0 + 3
-1x = 0 + 3

Combine like terms: 0 + 3 = 3
-1x = 3

Divide each side by '-1'.
x = -3

Simplifying
x = -3

Subproblem 2
Set the factor '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {-3, 7}

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