(x-3)(4x+1)=-3(x-3)(-x+7)

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Solution for (x-3)(4x+1)=-3(x-3)(-x+7) equation: 


Simplifying
(x + -3)(4x + 1) = -3(x + -3)(-1x + 7)

Reorder the terms:
(-3 + x)(4x + 1) = -3(x + -3)(-1x + 7)

Reorder the terms:
(-3 + x)(1 + 4x) = -3(x + -3)(-1x + 7)

Multiply (-3 + x) * (1 + 4x)
(-3(1 + 4x) + x(1 + 4x)) = -3(x + -3)(-1x + 7)
((1 * -3 + 4x * -3) + x(1 + 4x)) = -3(x + -3)(-1x + 7)
((-3 + -12x) + x(1 + 4x)) = -3(x + -3)(-1x + 7)
(-3 + -12x + (1 * x + 4x * x)) = -3(x + -3)(-1x + 7)
(-3 + -12x + (1x + 4x2)) = -3(x + -3)(-1x + 7)

Combine like terms: -12x + 1x = -11x
(-3 + -11x + 4x2) = -3(x + -3)(-1x + 7)

Reorder the terms:
-3 + -11x + 4x2 = -3(-3 + x)(-1x + 7)

Reorder the terms:
-3 + -11x + 4x2 = -3(-3 + x)(7 + -1x)

Multiply (-3 + x) * (7 + -1x)
-3 + -11x + 4x2 = -3(-3(7 + -1x) + x(7 + -1x))
-3 + -11x + 4x2 = -3((7 * -3 + -1x * -3) + x(7 + -1x))
-3 + -11x + 4x2 = -3((-21 + 3x) + x(7 + -1x))
-3 + -11x + 4x2 = -3(-21 + 3x + (7 * x + -1x * x))
-3 + -11x + 4x2 = -3(-21 + 3x + (7x + -1x2))

Combine like terms: 3x + 7x = 10x
-3 + -11x + 4x2 = -3(-21 + 10x + -1x2)
-3 + -11x + 4x2 = (-21 * -3 + 10x * -3 + -1x2 * -3)
-3 + -11x + 4x2 = (63 + -30x + 3x2)

Solving
-3 + -11x + 4x2 = 63 + -30x + 3x2

Solving for variable 'x'.

Reorder the terms:
-3 + -63 + -11x + 30x + 4x2 + -3x2 = 63 + -30x + 3x2 + -63 + 30x + -3x2

Combine like terms: -3 + -63 = -66
-66 + -11x + 30x + 4x2 + -3x2 = 63 + -30x + 3x2 + -63 + 30x + -3x2

Combine like terms: -11x + 30x = 19x
-66 + 19x + 4x2 + -3x2 = 63 + -30x + 3x2 + -63 + 30x + -3x2

Combine like terms: 4x2 + -3x2 = 1x2
-66 + 19x + 1x2 = 63 + -30x + 3x2 + -63 + 30x + -3x2

Reorder the terms:
-66 + 19x + 1x2 = 63 + -63 + -30x + 30x + 3x2 + -3x2

Combine like terms: 63 + -63 = 0
-66 + 19x + 1x2 = 0 + -30x + 30x + 3x2 + -3x2
-66 + 19x + 1x2 = -30x + 30x + 3x2 + -3x2

Combine like terms: -30x + 30x = 0
-66 + 19x + 1x2 = 0 + 3x2 + -3x2
-66 + 19x + 1x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
-66 + 19x + 1x2 = 0

Factor a trinomial.
(-22 + -1x)(3 + -1x) = 0


Subproblem 1
Set the factor '(-22 + -1x)' equal to zero and attempt to solve:

Simplifying
-22 + -1x = 0

Solving
-22 + -1x = 0

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

Add '22' to each side of the equation.
-22 + 22 + -1x = 0 + 22

Combine like terms: -22 + 22 = 0
0 + -1x = 0 + 22
-1x = 0 + 22

Combine like terms: 0 + 22 = 22
-1x = 22

Divide each side by '-1'.
x = -22

Simplifying
x = -22

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 = {-22, 3}

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