4x(x-7)=19x^2-29x

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Solution for 4x(x-7)=19x^2-29x equation:


Simplifying
4x(x + -7) = 19x2 + -29x

Reorder the terms:
4x(-7 + x) = 19x2 + -29x
(-7 * 4x + x * 4x) = 19x2 + -29x
(-28x + 4x2) = 19x2 + -29x

Reorder the terms:
-28x + 4x2 = -29x + 19x2

Solving
-28x + 4x2 = -29x + 19x2

Solving for variable 'x'.

Reorder the terms:
-28x + 29x + 4x2 + -19x2 = -29x + 19x2 + 29x + -19x2

Combine like terms: -28x + 29x = 1x
1x + 4x2 + -19x2 = -29x + 19x2 + 29x + -19x2

Combine like terms: 4x2 + -19x2 = -15x2
1x + -15x2 = -29x + 19x2 + 29x + -19x2

Reorder the terms:
1x + -15x2 = -29x + 29x + 19x2 + -19x2

Combine like terms: -29x + 29x = 0
1x + -15x2 = 0 + 19x2 + -19x2
1x + -15x2 = 19x2 + -19x2

Combine like terms: 19x2 + -19x2 = 0
1x + -15x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(1 + -15x) = 0

Subproblem 1

Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0

Subproblem 2

Set the factor '(1 + -15x)' equal to zero and attempt to solve: Simplifying 1 + -15x = 0 Solving 1 + -15x = 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 + -15x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -15x = 0 + -1 -15x = 0 + -1 Combine like terms: 0 + -1 = -1 -15x = -1 Divide each side by '-15'. x = 0.06666666667 Simplifying x = 0.06666666667

Solution

x = {0, 0.06666666667}

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