(3x-7)(8x+4)=0

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Solution for (3x-7)(8x+4)=0 equation:


Simplifying
(3x + -7)(8x + 4) = 0

Reorder the terms:
(-7 + 3x)(8x + 4) = 0

Reorder the terms:
(-7 + 3x)(4 + 8x) = 0

Multiply (-7 + 3x) * (4 + 8x)
(-7(4 + 8x) + 3x * (4 + 8x)) = 0
((4 * -7 + 8x * -7) + 3x * (4 + 8x)) = 0
((-28 + -56x) + 3x * (4 + 8x)) = 0
(-28 + -56x + (4 * 3x + 8x * 3x)) = 0
(-28 + -56x + (12x + 24x2)) = 0

Combine like terms: -56x + 12x = -44x
(-28 + -44x + 24x2) = 0

Solving
-28 + -44x + 24x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-7 + -11x + 6x2) = 0

Factor a trinomial.
4((-1 + -2x)(7 + -3x)) = 0

Ignore the factor 4.

Subproblem 1

Set the factor '(-1 + -2x)' equal to zero and attempt to solve: Simplifying -1 + -2x = 0 Solving -1 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -2x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -2x = 0 + 1 -2x = 0 + 1 Combine like terms: 0 + 1 = 1 -2x = 1 Divide each side by '-2'. x = -0.5 Simplifying x = -0.5

Subproblem 2

Set the factor '(7 + -3x)' equal to zero and attempt to solve: Simplifying 7 + -3x = 0 Solving 7 + -3x = 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 + -3x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -3x = 0 + -7 -3x = 0 + -7 Combine like terms: 0 + -7 = -7 -3x = -7 Divide each side by '-3'. x = 2.333333333 Simplifying x = 2.333333333

Solution

x = {-0.5, 2.333333333}

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