(x+2)(4x-9)=(2x+3)(3x-10)

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Solution for (x+2)(4x-9)=(2x+3)(3x-10) equation: 


Simplifying
(x + 2)(4x + -9) = (2x + 3)(3x + -10)

Reorder the terms:
(2 + x)(4x + -9) = (2x + 3)(3x + -10)

Reorder the terms:
(2 + x)(-9 + 4x) = (2x + 3)(3x + -10)

Multiply (2 + x) * (-9 + 4x)
(2(-9 + 4x) + x(-9 + 4x)) = (2x + 3)(3x + -10)
((-9 * 2 + 4x * 2) + x(-9 + 4x)) = (2x + 3)(3x + -10)
((-18 + 8x) + x(-9 + 4x)) = (2x + 3)(3x + -10)
(-18 + 8x + (-9 * x + 4x * x)) = (2x + 3)(3x + -10)
(-18 + 8x + (-9x + 4x2)) = (2x + 3)(3x + -10)

Combine like terms: 8x + -9x = -1x
(-18 + -1x + 4x2) = (2x + 3)(3x + -10)

Reorder the terms:
-18 + -1x + 4x2 = (3 + 2x)(3x + -10)

Reorder the terms:
-18 + -1x + 4x2 = (3 + 2x)(-10 + 3x)

Multiply (3 + 2x) * (-10 + 3x)
-18 + -1x + 4x2 = (3(-10 + 3x) + 2x * (-10 + 3x))
-18 + -1x + 4x2 = ((-10 * 3 + 3x * 3) + 2x * (-10 + 3x))
-18 + -1x + 4x2 = ((-30 + 9x) + 2x * (-10 + 3x))
-18 + -1x + 4x2 = (-30 + 9x + (-10 * 2x + 3x * 2x))
-18 + -1x + 4x2 = (-30 + 9x + (-20x + 6x2))

Combine like terms: 9x + -20x = -11x
-18 + -1x + 4x2 = (-30 + -11x + 6x2)

Solving
-18 + -1x + 4x2 = -30 + -11x + 6x2

Solving for variable 'x'.

Reorder the terms:
-18 + 30 + -1x + 11x + 4x2 + -6x2 = -30 + -11x + 6x2 + 30 + 11x + -6x2

Combine like terms: -18 + 30 = 12
12 + -1x + 11x + 4x2 + -6x2 = -30 + -11x + 6x2 + 30 + 11x + -6x2

Combine like terms: -1x + 11x = 10x
12 + 10x + 4x2 + -6x2 = -30 + -11x + 6x2 + 30 + 11x + -6x2

Combine like terms: 4x2 + -6x2 = -2x2
12 + 10x + -2x2 = -30 + -11x + 6x2 + 30 + 11x + -6x2

Reorder the terms:
12 + 10x + -2x2 = -30 + 30 + -11x + 11x + 6x2 + -6x2

Combine like terms: -30 + 30 = 0
12 + 10x + -2x2 = 0 + -11x + 11x + 6x2 + -6x2
12 + 10x + -2x2 = -11x + 11x + 6x2 + -6x2

Combine like terms: -11x + 11x = 0
12 + 10x + -2x2 = 0 + 6x2 + -6x2
12 + 10x + -2x2 = 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
12 + 10x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(6 + 5x + -1x2) = 0

Factor a trinomial.
2((6 + -1x)(1 + x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6

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

Simplifying
1 + x = 0

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

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

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

Simplifying
x = -1
Solution
x = {6, -1}

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