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

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


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

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

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

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

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

Solving
-30 + 17x + 2x2 = 54

Solving for variable 'x'.

Reorder the terms:
-30 + -54 + 17x + 2x2 = 54 + -54

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

Combine like terms: 54 + -54 = 0
-84 + 17x + 2x2 = 0

Factor a trinomial.
(-12 + -1x)(7 + -2x) = 0


Subproblem 1
Set the factor '(-12 + -1x)' equal to zero and attempt to solve:

Simplifying
-12 + -1x = 0

Solving
-12 + -1x = 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 + -1x = 0 + 12

Combine like terms: -12 + 12 = 0
0 + -1x = 0 + 12
-1x = 0 + 12

Combine like terms: 0 + 12 = 12
-1x = 12

Divide each side by '-1'.
x = -12

Simplifying
x = -12

Subproblem 2
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
Solution
x = {-12, 3.5}

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