(7x-3)(8x+2)=0

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Solution for (7x-3)(8x+2)=0 equation:


Simplifying
(7x + -3)(8x + 2) = 0

Reorder the terms:
(-3 + 7x)(8x + 2) = 0

Reorder the terms:
(-3 + 7x)(2 + 8x) = 0

Multiply (-3 + 7x) * (2 + 8x)
(-3(2 + 8x) + 7x * (2 + 8x)) = 0
((2 * -3 + 8x * -3) + 7x * (2 + 8x)) = 0
((-6 + -24x) + 7x * (2 + 8x)) = 0
(-6 + -24x + (2 * 7x + 8x * 7x)) = 0
(-6 + -24x + (14x + 56x2)) = 0

Combine like terms: -24x + 14x = -10x
(-6 + -10x + 56x2) = 0

Solving
-6 + -10x + 56x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + -5x + 28x2) = 0

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

Ignore the factor 2.

Subproblem 1

Set the factor '(-1 + -4x)' equal to zero and attempt to solve: Simplifying -1 + -4x = 0 Solving -1 + -4x = 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 + -4x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -4x = 0 + 1 -4x = 0 + 1 Combine like terms: 0 + 1 = 1 -4x = 1 Divide each side by '-4'. x = -0.25 Simplifying x = -0.25

Subproblem 2

Set the factor '(3 + -7x)' equal to zero and attempt to solve: Simplifying 3 + -7x = 0 Solving 3 + -7x = 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 + -7x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -7x = 0 + -3 -7x = 0 + -3 Combine like terms: 0 + -3 = -3 -7x = -3 Divide each side by '-7'. x = 0.4285714286 Simplifying x = 0.4285714286

Solution

x = {-0.25, 0.4285714286}

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