(x-7)(x+4)=0

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Solution for (x-7)(x+4)=0 equation:


Simplifying
(x + -7)(x + 4) = 0

Reorder the terms:
(-7 + x)(x + 4) = 0

Reorder the terms:
(-7 + x)(4 + x) = 0

Multiply (-7 + x) * (4 + x)
(-7(4 + x) + x(4 + x)) = 0
((4 * -7 + x * -7) + x(4 + x)) = 0
((-28 + -7x) + x(4 + x)) = 0
(-28 + -7x + (4 * x + x * x)) = 0
(-28 + -7x + (4x + x2)) = 0

Combine like terms: -7x + 4x = -3x
(-28 + -3x + x2) = 0

Solving
-28 + -3x + x2 = 0

Solving for variable 'x'.

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

Subproblem 1

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

Subproblem 2

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

Solution

x = {-4, 7}

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