(x-4)(x+7)=80

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Solution for (x-4)(x+7)=80 equation:


Simplifying
(x + -4)(x + 7) = 80

Reorder the terms:
(-4 + x)(x + 7) = 80

Reorder the terms:
(-4 + x)(7 + x) = 80

Multiply (-4 + x) * (7 + x)
(-4(7 + x) + x(7 + x)) = 80
((7 * -4 + x * -4) + x(7 + x)) = 80
((-28 + -4x) + x(7 + x)) = 80
(-28 + -4x + (7 * x + x * x)) = 80
(-28 + -4x + (7x + x2)) = 80

Combine like terms: -4x + 7x = 3x
(-28 + 3x + x2) = 80

Solving
-28 + 3x + x2 = 80

Solving for variable 'x'.

Reorder the terms:
-28 + -80 + 3x + x2 = 80 + -80

Combine like terms: -28 + -80 = -108
-108 + 3x + x2 = 80 + -80

Combine like terms: 80 + -80 = 0
-108 + 3x + x2 = 0

Factor a trinomial.
(-12 + -1x)(9 + -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 '(9 + -1x)' equal to zero and attempt to solve:

Simplifying
9 + -1x = 0

Solving
9 + -1x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1x = 0 + -9

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

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

Divide each side by '-1'.
x = 9

Simplifying
x = 9
Solution
x = {-12, 9}

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