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

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


Simplifying
(7 + -1x)(2x + 3) = 0

Reorder the terms:
(7 + -1x)(3 + 2x) = 0

Multiply (7 + -1x) * (3 + 2x)
(7(3 + 2x) + -1x * (3 + 2x)) = 0
((3 * 7 + 2x * 7) + -1x * (3 + 2x)) = 0
((21 + 14x) + -1x * (3 + 2x)) = 0
(21 + 14x + (3 * -1x + 2x * -1x)) = 0
(21 + 14x + (-3x + -2x2)) = 0

Combine like terms: 14x + -3x = 11x
(21 + 11x + -2x2) = 0

Solving
21 + 11x + -2x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(7 + -1x)(3 + 2x) = 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 '(3 + 2x)' equal to zero and attempt to solve: Simplifying 3 + 2x = 0 Solving 3 + 2x = 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 + 2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2x = 0 + -3 2x = 0 + -3 Combine like terms: 0 + -3 = -3 2x = -3 Divide each side by '2'. x = -1.5 Simplifying x = -1.5

Solution

x = {7, -1.5}

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