(x-5)(4x+4)=3x(x-3)+10

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Solution for (x-5)(4x+4)=3x(x-3)+10 equation: 


Simplifying
(x + -5)(4x + 4) = 3x(x + -3) + 10

Reorder the terms:
(-5 + x)(4x + 4) = 3x(x + -3) + 10

Reorder the terms:
(-5 + x)(4 + 4x) = 3x(x + -3) + 10

Multiply (-5 + x) * (4 + 4x)
(-5(4 + 4x) + x(4 + 4x)) = 3x(x + -3) + 10
((4 * -5 + 4x * -5) + x(4 + 4x)) = 3x(x + -3) + 10
((-20 + -20x) + x(4 + 4x)) = 3x(x + -3) + 10
(-20 + -20x + (4 * x + 4x * x)) = 3x(x + -3) + 10
(-20 + -20x + (4x + 4x2)) = 3x(x + -3) + 10

Combine like terms: -20x + 4x = -16x
(-20 + -16x + 4x2) = 3x(x + -3) + 10

Reorder the terms:
-20 + -16x + 4x2 = 3x(-3 + x) + 10
-20 + -16x + 4x2 = (-3 * 3x + x * 3x) + 10
-20 + -16x + 4x2 = (-9x + 3x2) + 10

Reorder the terms:
-20 + -16x + 4x2 = 10 + -9x + 3x2

Solving
-20 + -16x + 4x2 = 10 + -9x + 3x2

Solving for variable 'x'.

Reorder the terms:
-20 + -10 + -16x + 9x + 4x2 + -3x2 = 10 + -9x + 3x2 + -10 + 9x + -3x2

Combine like terms: -20 + -10 = -30
-30 + -16x + 9x + 4x2 + -3x2 = 10 + -9x + 3x2 + -10 + 9x + -3x2

Combine like terms: -16x + 9x = -7x
-30 + -7x + 4x2 + -3x2 = 10 + -9x + 3x2 + -10 + 9x + -3x2

Combine like terms: 4x2 + -3x2 = 1x2
-30 + -7x + 1x2 = 10 + -9x + 3x2 + -10 + 9x + -3x2

Reorder the terms:
-30 + -7x + 1x2 = 10 + -10 + -9x + 9x + 3x2 + -3x2

Combine like terms: 10 + -10 = 0
-30 + -7x + 1x2 = 0 + -9x + 9x + 3x2 + -3x2
-30 + -7x + 1x2 = -9x + 9x + 3x2 + -3x2

Combine like terms: -9x + 9x = 0
-30 + -7x + 1x2 = 0 + 3x2 + -3x2
-30 + -7x + 1x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
-30 + -7x + 1x2 = 0

Factor a trinomial.
(-3 + -1x)(10 + -1x) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(10 + -1x)' equal to zero and attempt to solve:

Simplifying
10 + -1x = 0

Solving
10 + -1x = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1x = 0 + -10
-1x = 0 + -10

Combine like terms: 0 + -10 = -10
-1x = -10

Divide each side by '-1'.
x = 10

Simplifying
x = 10
Solution
x = {-3, 10}

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