=(x+3)(x-7)

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Solution for =(x+3)(x-7) equation:


Simplifying
0 = (x + 3)(x + -7)

Reorder the terms:
0 = (3 + x)(x + -7)

Reorder the terms:
0 = (3 + x)(-7 + x)

Multiply (3 + x) * (-7 + x)
0 = (3(-7 + x) + x(-7 + x))
0 = ((-7 * 3 + x * 3) + x(-7 + x))
0 = ((-21 + 3x) + x(-7 + x))
0 = (-21 + 3x + (-7 * x + x * x))
0 = (-21 + 3x + (-7x + x2))

Combine like terms: 3x + -7x = -4x
0 = (-21 + -4x + x2)

Solving
0 = -21 + -4x + x2

Solving for variable 'x'.

Combine like terms: 0 + 21 = 21
21 + 4x + -1x2 = -21 + -4x + x2 + 21 + 4x + -1x2

Reorder the terms:
21 + 4x + -1x2 = -21 + 21 + -4x + 4x + x2 + -1x2

Combine like terms: -21 + 21 = 0
21 + 4x + -1x2 = 0 + -4x + 4x + x2 + -1x2
21 + 4x + -1x2 = -4x + 4x + x2 + -1x2

Combine like terms: -4x + 4x = 0
21 + 4x + -1x2 = 0 + x2 + -1x2
21 + 4x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
21 + 4x + -1x2 = 0

Factor a trinomial.
(7 + -1x)(3 + x) = 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 '(3 + x)' equal to zero and attempt to solve: Simplifying 3 + x = 0 Solving 3 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + x = 0 + -3 x = 0 + -3 Combine like terms: 0 + -3 = -3 x = -3 Simplifying x = -3

Solution

x = {7, -3}

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