(x+3)(x-4)=x+23

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Solution for (x+3)(x-4)=x+23 equation:


Simplifying
(x + 3)(x + -4) = x + 23

Reorder the terms:
(3 + x)(x + -4) = x + 23

Reorder the terms:
(3 + x)(-4 + x) = x + 23

Multiply (3 + x) * (-4 + x)
(3(-4 + x) + x(-4 + x)) = x + 23
((-4 * 3 + x * 3) + x(-4 + x)) = x + 23
((-12 + 3x) + x(-4 + x)) = x + 23
(-12 + 3x + (-4 * x + x * x)) = x + 23
(-12 + 3x + (-4x + x2)) = x + 23

Combine like terms: 3x + -4x = -1x
(-12 + -1x + x2) = x + 23

Reorder the terms:
-12 + -1x + x2 = 23 + x

Solving
-12 + -1x + x2 = 23 + x

Solving for variable 'x'.

Reorder the terms:
-12 + -23 + -1x + -1x + x2 = 23 + x + -23 + -1x

Combine like terms: -12 + -23 = -35
-35 + -1x + -1x + x2 = 23 + x + -23 + -1x

Combine like terms: -1x + -1x = -2x
-35 + -2x + x2 = 23 + x + -23 + -1x

Reorder the terms:
-35 + -2x + x2 = 23 + -23 + x + -1x

Combine like terms: 23 + -23 = 0
-35 + -2x + x2 = 0 + x + -1x
-35 + -2x + x2 = x + -1x

Combine like terms: x + -1x = 0
-35 + -2x + x2 = 0

Factor a trinomial.
(-5 + -1x)(7 + -1x) = 0

Subproblem 1

Set the factor '(-5 + -1x)' equal to zero and attempt to solve: Simplifying -5 + -1x = 0 Solving -5 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -1x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1x = 0 + 5 -1x = 0 + 5 Combine like terms: 0 + 5 = 5 -1x = 5 Divide each side by '-1'. x = -5 Simplifying x = -5

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 = {-5, 7}

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