(2x+18)(x-4)=x(x+9)+60

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Solution for (2x+18)(x-4)=x(x+9)+60 equation:


Simplifying
(2x + 18)(x + -4) = x(x + 9) + 60

Reorder the terms:
(18 + 2x)(x + -4) = x(x + 9) + 60

Reorder the terms:
(18 + 2x)(-4 + x) = x(x + 9) + 60

Multiply (18 + 2x) * (-4 + x)
(18(-4 + x) + 2x * (-4 + x)) = x(x + 9) + 60
((-4 * 18 + x * 18) + 2x * (-4 + x)) = x(x + 9) + 60
((-72 + 18x) + 2x * (-4 + x)) = x(x + 9) + 60
(-72 + 18x + (-4 * 2x + x * 2x)) = x(x + 9) + 60
(-72 + 18x + (-8x + 2x2)) = x(x + 9) + 60

Combine like terms: 18x + -8x = 10x
(-72 + 10x + 2x2) = x(x + 9) + 60

Reorder the terms:
-72 + 10x + 2x2 = x(9 + x) + 60
-72 + 10x + 2x2 = (9 * x + x * x) + 60
-72 + 10x + 2x2 = (9x + x2) + 60

Reorder the terms:
-72 + 10x + 2x2 = 60 + 9x + x2

Solving
-72 + 10x + 2x2 = 60 + 9x + x2

Solving for variable 'x'.

Reorder the terms:
-72 + -60 + 10x + -9x + 2x2 + -1x2 = 60 + 9x + x2 + -60 + -9x + -1x2

Combine like terms: -72 + -60 = -132
-132 + 10x + -9x + 2x2 + -1x2 = 60 + 9x + x2 + -60 + -9x + -1x2

Combine like terms: 10x + -9x = 1x
-132 + 1x + 2x2 + -1x2 = 60 + 9x + x2 + -60 + -9x + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
-132 + 1x + 1x2 = 60 + 9x + x2 + -60 + -9x + -1x2

Reorder the terms:
-132 + 1x + 1x2 = 60 + -60 + 9x + -9x + x2 + -1x2

Combine like terms: 60 + -60 = 0
-132 + 1x + 1x2 = 0 + 9x + -9x + x2 + -1x2
-132 + 1x + 1x2 = 9x + -9x + x2 + -1x2

Combine like terms: 9x + -9x = 0
-132 + 1x + 1x2 = 0 + x2 + -1x2
-132 + 1x + 1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-132 + 1x + 1x2 = 0

Factor a trinomial.
(-12 + -1x)(11 + -1x) = 0

Subproblem 1

Set the factor '(-12 + -1x)' equal to zero and attempt to solve: Simplifying -12 + -1x = 0 Solving -12 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + -1x = 0 + 12 Combine like terms: -12 + 12 = 0 0 + -1x = 0 + 12 -1x = 0 + 12 Combine like terms: 0 + 12 = 12 -1x = 12 Divide each side by '-1'. x = -12 Simplifying x = -12

Subproblem 2

Set the factor '(11 + -1x)' equal to zero and attempt to solve: Simplifying 11 + -1x = 0 Solving 11 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + -1x = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -1x = 0 + -11 -1x = 0 + -11 Combine like terms: 0 + -11 = -11 -1x = -11 Divide each side by '-1'. x = 11 Simplifying x = 11

Solution

x = {-12, 11}

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