(x-7)(x+9)=-(x+35)

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Solution for (x-7)(x+9)=-(x+35) equation: 


Simplifying
(x + -7)(x + 9) = -1(x + 35)

Reorder the terms:
(-7 + x)(x + 9) = -1(x + 35)

Reorder the terms:
(-7 + x)(9 + x) = -1(x + 35)

Multiply (-7 + x) * (9 + x)
(-7(9 + x) + x(9 + x)) = -1(x + 35)
((9 * -7 + x * -7) + x(9 + x)) = -1(x + 35)
((-63 + -7x) + x(9 + x)) = -1(x + 35)
(-63 + -7x + (9 * x + x * x)) = -1(x + 35)
(-63 + -7x + (9x + x2)) = -1(x + 35)

Combine like terms: -7x + 9x = 2x
(-63 + 2x + x2) = -1(x + 35)

Reorder the terms:
-63 + 2x + x2 = -1(35 + x)
-63 + 2x + x2 = (35 * -1 + x * -1)
-63 + 2x + x2 = (-35 + -1x)

Solving
-63 + 2x + x2 = -35 + -1x

Solving for variable 'x'.

Reorder the terms:
-63 + 35 + 2x + x + x2 = -35 + -1x + 35 + x

Combine like terms: -63 + 35 = -28
-28 + 2x + x + x2 = -35 + -1x + 35 + x

Combine like terms: 2x + x = 3x
-28 + 3x + x2 = -35 + -1x + 35 + x

Reorder the terms:
-28 + 3x + x2 = -35 + 35 + -1x + x

Combine like terms: -35 + 35 = 0
-28 + 3x + x2 = 0 + -1x + x
-28 + 3x + x2 = -1x + x

Combine like terms: -1x + x = 0
-28 + 3x + x2 = 0

Factor a trinomial.
(-7 + -1x)(4 + -1x) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {-7, 4}

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