(4x+23)(x-9)=(3x+21)(x-10)

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Solution for (4x+23)(x-9)=(3x+21)(x-10) equation:


Simplifying
(4x + 23)(x + -9) = (3x + 21)(x + -10)

Reorder the terms:
(23 + 4x)(x + -9) = (3x + 21)(x + -10)

Reorder the terms:
(23 + 4x)(-9 + x) = (3x + 21)(x + -10)

Multiply (23 + 4x) * (-9 + x)
(23(-9 + x) + 4x * (-9 + x)) = (3x + 21)(x + -10)
((-9 * 23 + x * 23) + 4x * (-9 + x)) = (3x + 21)(x + -10)
((-207 + 23x) + 4x * (-9 + x)) = (3x + 21)(x + -10)
(-207 + 23x + (-9 * 4x + x * 4x)) = (3x + 21)(x + -10)
(-207 + 23x + (-36x + 4x2)) = (3x + 21)(x + -10)

Combine like terms: 23x + -36x = -13x
(-207 + -13x + 4x2) = (3x + 21)(x + -10)

Reorder the terms:
-207 + -13x + 4x2 = (21 + 3x)(x + -10)

Reorder the terms:
-207 + -13x + 4x2 = (21 + 3x)(-10 + x)

Multiply (21 + 3x) * (-10 + x)
-207 + -13x + 4x2 = (21(-10 + x) + 3x * (-10 + x))
-207 + -13x + 4x2 = ((-10 * 21 + x * 21) + 3x * (-10 + x))
-207 + -13x + 4x2 = ((-210 + 21x) + 3x * (-10 + x))
-207 + -13x + 4x2 = (-210 + 21x + (-10 * 3x + x * 3x))
-207 + -13x + 4x2 = (-210 + 21x + (-30x + 3x2))

Combine like terms: 21x + -30x = -9x
-207 + -13x + 4x2 = (-210 + -9x + 3x2)

Solving
-207 + -13x + 4x2 = -210 + -9x + 3x2

Solving for variable 'x'.

Reorder the terms:
-207 + 210 + -13x + 9x + 4x2 + -3x2 = -210 + -9x + 3x2 + 210 + 9x + -3x2

Combine like terms: -207 + 210 = 3
3 + -13x + 9x + 4x2 + -3x2 = -210 + -9x + 3x2 + 210 + 9x + -3x2

Combine like terms: -13x + 9x = -4x
3 + -4x + 4x2 + -3x2 = -210 + -9x + 3x2 + 210 + 9x + -3x2

Combine like terms: 4x2 + -3x2 = 1x2
3 + -4x + 1x2 = -210 + -9x + 3x2 + 210 + 9x + -3x2

Reorder the terms:
3 + -4x + 1x2 = -210 + 210 + -9x + 9x + 3x2 + -3x2

Combine like terms: -210 + 210 = 0
3 + -4x + 1x2 = 0 + -9x + 9x + 3x2 + -3x2
3 + -4x + 1x2 = -9x + 9x + 3x2 + -3x2

Combine like terms: -9x + 9x = 0
3 + -4x + 1x2 = 0 + 3x2 + -3x2
3 + -4x + 1x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
3 + -4x + 1x2 = 0

Factor a trinomial.
(1 + -1x)(3 + -1x) = 0


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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

Simplifying
x = 1

Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 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 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {1, 3}

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