54=(x+10)(2x-3)

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Solution for 54=(x+10)(2x-3) equation: 


Simplifying
54 = (x + 10)(2x + -3)

Reorder the terms:
54 = (10 + x)(2x + -3)

Reorder the terms:
54 = (10 + x)(-3 + 2x)

Multiply (10 + x) * (-3 + 2x)
54 = (10(-3 + 2x) + x(-3 + 2x))
54 = ((-3 * 10 + 2x * 10) + x(-3 + 2x))
54 = ((-30 + 20x) + x(-3 + 2x))
54 = (-30 + 20x + (-3 * x + 2x * x))
54 = (-30 + 20x + (-3x + 2x2))

Combine like terms: 20x + -3x = 17x
54 = (-30 + 17x + 2x2)

Solving
54 = -30 + 17x + 2x2

Solving for variable 'x'.

Combine like terms: 54 + 30 = 84
84 + -17x + -2x2 = -30 + 17x + 2x2 + 30 + -17x + -2x2

Reorder the terms:
84 + -17x + -2x2 = -30 + 30 + 17x + -17x + 2x2 + -2x2

Combine like terms: -30 + 30 = 0
84 + -17x + -2x2 = 0 + 17x + -17x + 2x2 + -2x2
84 + -17x + -2x2 = 17x + -17x + 2x2 + -2x2

Combine like terms: 17x + -17x = 0
84 + -17x + -2x2 = 0 + 2x2 + -2x2
84 + -17x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
84 + -17x + -2x2 = 0

Factor a trinomial.
(7 + -2x)(12 + x) = 0


Subproblem 1
Set the factor '(7 + -2x)' equal to zero and attempt to solve:

Simplifying
7 + -2x = 0

Solving
7 + -2x = 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 + -2x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -2x = 0 + -7
-2x = 0 + -7

Combine like terms: 0 + -7 = -7
-2x = -7

Divide each side by '-2'.
x = 3.5

Simplifying
x = 3.5

Subproblem 2
Set the factor '(12 + x)' equal to zero and attempt to solve:

Simplifying
12 + x = 0

Solving
12 + x = 0

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

Add '-12' to each side of the equation.
12 + -12 + x = 0 + -12

Combine like terms: 12 + -12 = 0
0 + x = 0 + -12
x = 0 + -12

Combine like terms: 0 + -12 = -12
x = -12

Simplifying
x = -12
Solution
x = {3.5, -12}

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