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

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Solution for (7x-2)(2x+1)+3(7x-2)= equation:


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

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

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

Multiply (-2 + 7x) * (1 + 2x)
(-2(1 + 2x) + 7x * (1 + 2x)) + 3(7x + -2) = 0
((1 * -2 + 2x * -2) + 7x * (1 + 2x)) + 3(7x + -2) = 0
((-2 + -4x) + 7x * (1 + 2x)) + 3(7x + -2) = 0
(-2 + -4x + (1 * 7x + 2x * 7x)) + 3(7x + -2) = 0
(-2 + -4x + (7x + 14x2)) + 3(7x + -2) = 0

Combine like terms: -4x + 7x = 3x
(-2 + 3x + 14x2) + 3(7x + -2) = 0

Reorder the terms:
-2 + 3x + 14x2 + 3(-2 + 7x) = 0
-2 + 3x + 14x2 + (-2 * 3 + 7x * 3) = 0
-2 + 3x + 14x2 + (-6 + 21x) = 0

Reorder the terms:
-2 + -6 + 3x + 21x + 14x2 = 0

Combine like terms: -2 + -6 = -8
-8 + 3x + 21x + 14x2 = 0

Combine like terms: 3x + 21x = 24x
-8 + 24x + 14x2 = 0

Solving
-8 + 24x + 14x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-4 + 12x + 7x2) = 0

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

Ignore the factor 2.

Subproblem 1

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

Subproblem 2

Set the factor '(2 + -7x)' equal to zero and attempt to solve: Simplifying 2 + -7x = 0 Solving 2 + -7x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -7x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -7x = 0 + -2 -7x = 0 + -2 Combine like terms: 0 + -2 = -2 -7x = -2 Divide each side by '-7'. x = 0.2857142857 Simplifying x = 0.2857142857

Solution

x = {-2, 0.2857142857}

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