(x+4)(x-7)=180

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Solution for (x+4)(x-7)=180 equation: 


Simplifying
(x + 4)(x + -7) = 180

Reorder the terms:
(4 + x)(x + -7) = 180

Reorder the terms:
(4 + x)(-7 + x) = 180

Multiply (4 + x) * (-7 + x)
(4(-7 + x) + x(-7 + x)) = 180
((-7 * 4 + x * 4) + x(-7 + x)) = 180
((-28 + 4x) + x(-7 + x)) = 180
(-28 + 4x + (-7 * x + x * x)) = 180
(-28 + 4x + (-7x + x2)) = 180

Combine like terms: 4x + -7x = -3x
(-28 + -3x + x2) = 180

Solving
-28 + -3x + x2 = 180

Solving for variable 'x'.

Reorder the terms:
-28 + -180 + -3x + x2 = 180 + -180

Combine like terms: -28 + -180 = -208
-208 + -3x + x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-208 + -3x + x2 = 0

Factor a trinomial.
(-13 + -1x)(16 + -1x) = 0


Subproblem 1
Set the factor '(-13 + -1x)' equal to zero and attempt to solve:

Simplifying
-13 + -1x = 0

Solving
-13 + -1x = 0

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

Add '13' to each side of the equation.
-13 + 13 + -1x = 0 + 13

Combine like terms: -13 + 13 = 0
0 + -1x = 0 + 13
-1x = 0 + 13

Combine like terms: 0 + 13 = 13
-1x = 13

Divide each side by '-1'.
x = -13

Simplifying
x = -13

Subproblem 2
Set the factor '(16 + -1x)' equal to zero and attempt to solve:

Simplifying
16 + -1x = 0

Solving
16 + -1x = 0

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

Add '-16' to each side of the equation.
16 + -16 + -1x = 0 + -16

Combine like terms: 16 + -16 = 0
0 + -1x = 0 + -16
-1x = 0 + -16

Combine like terms: 0 + -16 = -16
-1x = -16

Divide each side by '-1'.
x = 16

Simplifying
x = 16
Solution
x = {-13, 16}

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