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

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


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

Reorder the terms:
4(4 + x) = (x + -3)(x + 4)
(4 * 4 + x * 4) = (x + -3)(x + 4)
(16 + 4x) = (x + -3)(x + 4)

Reorder the terms:
16 + 4x = (-3 + x)(x + 4)

Reorder the terms:
16 + 4x = (-3 + x)(4 + x)

Multiply (-3 + x) * (4 + x)
16 + 4x = (-3(4 + x) + x(4 + x))
16 + 4x = ((4 * -3 + x * -3) + x(4 + x))
16 + 4x = ((-12 + -3x) + x(4 + x))
16 + 4x = (-12 + -3x + (4 * x + x * x))
16 + 4x = (-12 + -3x + (4x + x2))

Combine like terms: -3x + 4x = 1x
16 + 4x = (-12 + 1x + x2)

Solving
16 + 4x = -12 + 1x + x2

Solving for variable 'x'.

Reorder the terms:
16 + 12 + 4x + -1x + -1x2 = -12 + 1x + x2 + 12 + -1x + -1x2

Combine like terms: 16 + 12 = 28
28 + 4x + -1x + -1x2 = -12 + 1x + x2 + 12 + -1x + -1x2

Combine like terms: 4x + -1x = 3x
28 + 3x + -1x2 = -12 + 1x + x2 + 12 + -1x + -1x2

Reorder the terms:
28 + 3x + -1x2 = -12 + 12 + 1x + -1x + x2 + -1x2

Combine like terms: -12 + 12 = 0
28 + 3x + -1x2 = 0 + 1x + -1x + x2 + -1x2
28 + 3x + -1x2 = 1x + -1x + x2 + -1x2

Combine like terms: 1x + -1x = 0
28 + 3x + -1x2 = 0 + x2 + -1x2
28 + 3x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
28 + 3x + -1x2 = 0

Factor a trinomial.
(7 + -1x)(4 + x) = 0

Subproblem 1

Set the factor '(7 + -1x)' equal to zero and attempt to solve: Simplifying 7 + -1x = 0 Solving 7 + -1x = 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 + -1x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1x = 0 + -7 -1x = 0 + -7 Combine like terms: 0 + -7 = -7 -1x = -7 Divide each side by '-1'. x = 7 Simplifying x = 7

Subproblem 2

Set the factor '(4 + x)' equal to zero and attempt to solve: Simplifying 4 + x = 0 Solving 4 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + x = 0 + -4 x = 0 + -4 Combine like terms: 0 + -4 = -4 x = -4 Simplifying x = -4

Solution

x = {7, -4}

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