0=(7x+6)(x-4)

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Solution for 0=(7x+6)(x-4) equation:


Simplifying
0 = (7x + 6)(x + -4)

Reorder the terms:
0 = (6 + 7x)(x + -4)

Reorder the terms:
0 = (6 + 7x)(-4 + x)

Multiply (6 + 7x) * (-4 + x)
0 = (6(-4 + x) + 7x * (-4 + x))
0 = ((-4 * 6 + x * 6) + 7x * (-4 + x))
0 = ((-24 + 6x) + 7x * (-4 + x))
0 = (-24 + 6x + (-4 * 7x + x * 7x))
0 = (-24 + 6x + (-28x + 7x2))

Combine like terms: 6x + -28x = -22x
0 = (-24 + -22x + 7x2)

Solving
0 = -24 + -22x + 7x2

Solving for variable 'x'.

Combine like terms: 0 + 24 = 24
24 + 22x + -7x2 = -24 + -22x + 7x2 + 24 + 22x + -7x2

Reorder the terms:
24 + 22x + -7x2 = -24 + 24 + -22x + 22x + 7x2 + -7x2

Combine like terms: -24 + 24 = 0
24 + 22x + -7x2 = 0 + -22x + 22x + 7x2 + -7x2
24 + 22x + -7x2 = -22x + 22x + 7x2 + -7x2

Combine like terms: -22x + 22x = 0
24 + 22x + -7x2 = 0 + 7x2 + -7x2
24 + 22x + -7x2 = 7x2 + -7x2

Combine like terms: 7x2 + -7x2 = 0
24 + 22x + -7x2 = 0

Factor a trinomial.
(4 + -1x)(6 + 7x) = 0

Subproblem 1

Set the factor '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 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 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4

Subproblem 2

Set the factor '(6 + 7x)' equal to zero and attempt to solve: Simplifying 6 + 7x = 0 Solving 6 + 7x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + 7x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + 7x = 0 + -6 7x = 0 + -6 Combine like terms: 0 + -6 = -6 7x = -6 Divide each side by '7'. x = -0.8571428571 Simplifying x = -0.8571428571

Solution

x = {4, -0.8571428571}

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