(x-4)(x+5)=52

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Solution for (x-4)(x+5)=52 equation:


Simplifying
(x + -4)(x + 5) = 52

Reorder the terms:
(-4 + x)(x + 5) = 52

Reorder the terms:
(-4 + x)(5 + x) = 52

Multiply (-4 + x) * (5 + x)
(-4(5 + x) + x(5 + x)) = 52
((5 * -4 + x * -4) + x(5 + x)) = 52
((-20 + -4x) + x(5 + x)) = 52
(-20 + -4x + (5 * x + x * x)) = 52
(-20 + -4x + (5x + x2)) = 52

Combine like terms: -4x + 5x = 1x
(-20 + 1x + x2) = 52

Solving
-20 + 1x + x2 = 52

Solving for variable 'x'.

Reorder the terms:
-20 + -52 + 1x + x2 = 52 + -52

Combine like terms: -20 + -52 = -72
-72 + 1x + x2 = 52 + -52

Combine like terms: 52 + -52 = 0
-72 + 1x + x2 = 0

Factor a trinomial.
(-9 + -1x)(8 + -1x) = 0

Subproblem 1

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

Subproblem 2

Set the factor '(8 + -1x)' equal to zero and attempt to solve: Simplifying 8 + -1x = 0 Solving 8 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1x = 0 + -8 -1x = 0 + -8 Combine like terms: 0 + -8 = -8 -1x = -8 Divide each side by '-1'. x = 8 Simplifying x = 8

Solution

x = {-9, 8}

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